IB Physics Review-Waves

NAME______________________________ IB PHYSICS HL REVIEW PACKET: WAVES & VIBRATIONS 1.

This question is about waves and wave properties. (a)

By making reference to waves, distinguish between a ray and a wavefront . ............................ .......................................... ............................ .............................. .............................. ............................. .............................. ............................. ................. ... ............................ .......................................... ............................ .............................. .............................. ............................. .............................. ............................. ................. ... .............................. ............................................. ............................. ............................ ............................. ............................... .............................. ............................ ..............

(3)

The diagram below shows three wavefronts incident on a boundary between medium I and medium R. Wavefront CD is shown crossing the boundary. Wavefront EF is incomplete. A

C

E

F medium I medium R 

B

(b)

(i)

D

On the diagram above, draw a line to complete the wavefront EF. (1)

(ii)

Explain in which medium, I or R, the wave has the higher speed. ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... (3)

(iii)

By taking appropriate measurements measurements from the diagram, determine the ratio of the speeds of the wave travelling from medium I to medium R. ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... (2)

1

The graph below shows the variation with time t of t of the velocity v of one particle of the medium through which the wave is travelling. 8 6 4 2 v

/ ms –1 0

0

1

2

3

4

5

 –2

6

7 t  /

ms

 –4  –6  –8 (c)

(i)

Explain how it can be deduced from the graph that the particle is oscillating. ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... (2)

(ii)

Determine the frequency of oscillation of the particle. ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... (2)

(iii)

Mark on the graph with the letter M one time at which the particle is at maximum displacement. (1)

(iv)

Estimate the area between the curve and the x the x-axis -axis from the time t = t = 0 to the time t = t = 1.5 ms. ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... (2)

(v)

Suggest what the area in c (iv) represents. ............................ .......................................... ............................ ............................ ............................. ............................... ............................... ...................... ....... (1) (Total 17 marks)

2

2.

This question is about sound waves. A sound wave of frequency 660 Hz passes through air. The variation of particle displacement with distance along the wave at one instant of time is shown below.

0.5

displacement / mm

0 0

1.0

2.0

distance / m

 –0.5

(a)

State whether this wave is an example of a longitudinal or a transverse wave. ...........................................................................................................................

(b)

(1)

Using data from the above graph, deduce for this sound wave, (i)

the wavelength. ...........................................................................................................................

(ii)

the amplitude. ...........................................................................................................................

(iii)

(1)

(1)

the speed. ........................................................................................................................... ........................................................................................................................... ...........................................................................................................................

(2)

(Total 5 marks) 3.

This question is about waves and wave motion. (a)

(i)

Define what is meant by the speed of a wave. ........................................................................................................................... ...........................................................................................................................

(ii)

(2)

Light is emitted from a candle flame. Explain why, in this situation, it is correct to refer to the “speed of the emitted light”, rather than its velocity. ........................................................................................................................... ...........................................................................................................................

(b)

(i)

(2)

Define, by reference to wave motion, what is meant by displacement . ........................................................................................................................... ...........................................................................................................................

(2)

3

(ii)

By reference to displacement, describe the difference between a longitudinal wave and a transverse wave. ........................................................................................................................... ...........................................................................................................................

...........................................................................................................................

(3)

The centre of an earthquake produces both longitudinal waves (P waves) and transverse waves (S waves). The graph below shows the variation with time t of the distance d moved by the two types of wave. d /

km

S wave

P wave

1200

800

400

0 0

25

50

75

100

125

150

175

200

225 t /

(c)

s

Use the graph to determine the speed of  (i)

the P waves. ........................................................................................................................... ...........................................................................................................................

(ii)

(1)

the S waves. ........................................................................................................................... ...........................................................................................................................

(1)

The waves from an earthquake close to the Earth’s surface are detected at three laboratories L 1, L2 and L3. The laboratories are at the corners of a triangle so that each is separated from the others by a distance of 900 km, as shown in the diagram below.

900 km L1

L2

L3 The records of the variation with time of the vibrations produced by the earthquake as detected at the three laboratories are shown below. All three records were started at the same time. L1 L2

start of trace

L3 time 4

On each record, one pulse is made by the S wave and the other by the P wave. The separation of the two  pulses is referred to as the S-P interval. (d)

(i)

On the trace produced by laboratory L2, identify, by reference to your answers in (c), the pulse due to the P wave (label the pulse P).

(1) (ii)

Using evidence from the records of the earthquake, state which laboratory was closest to the site of the earthquake. ...........................................................................................................................

(1) (iii)

State three separate pieces of evidence for your statement in (d)(ii). (3) 1.

................................................................................................................. .................................................................................................................

2.

................................................................................................................. .................................................................................................................

3.

.................................................................................................................

................................................................................................................. (iv)

The S-P intervals are 68 s, 42 s and 27 s for laboratories L1, L2 and L3 respectively. Use the graph, or otherwise, to determine the distance of the earthquake from each laboratory. Explain your working. ........................................................................................................................... ........................................................................................................................... Distance from L1

= ......................km

........................................................................................................................... Distance from L2

= ......................km

........................................................................................................................... Distance from L3

= ......................km

...........................................................................................................................

(4) (v)

Mark on the diagram a possible site of the earthquake. (1)

5

There is a tall building near to the site of the earthquake, as illustrated below.

 building

ground  direction of vibrations The base of the building vibrates horizontally due to the earthquake.

(e)

(i)

On the diagram above, draw the fundamental mode of vibration of the building caused by these vibrations.

(1) The building is of height 280 m and the mean speed of waves in the structure of the building is 3.4 × 10 (ii)

3

 –1 ms .

Explain quantitatively why earthquake waves of frequency about 6 Hz are likely to be very destructive. ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... ........................................................................................................................... (3)

(Total 25 marks) 4.

This question is about the interference of waves. (a)

State the principle of superposition. ...................................................................................................................................... .....................................................................................................................................

(2)

A wire is stretched between two points A and B.

B

A

A standing wave is set up in the wire. This wave can be thought of as being made up from the superposition of two waves, a wave X travelling from A to B and a wave Y travelling from B to A. At one particular instant in time, the displacement of the wire is as shown. A background grid is given for reference and the equilibrium position of the wire is shown as a dotted line.

A

B

6

(b)

On the grids below, draw the displacement of the wire due to wave X and wave Y. Wave X

B

A

Wave Y

B

A

(4) The diagram below shows an arrangement (not to scale) for observing the interference pattern produced by the superposition of two light waves.

P

S1 monochromatic light source

O

S S2

single slit

double slit

Screen

S1 and S2 are two very narrow slits. The single slit S ensures that the light leaving the slits S1 and S2 is coherent. (c)

(i)

Define coherent . ........................................................................................................................... ...........................................................................................................................

(1) (ii)

Explain why the slits S1 and S2 need to be very narrow. ........................................................................................................................... ...........................................................................................................................

(2) (Total 9 marks) 7

5.

This question is about wave properties and interference. The diagram below represents the direction of oscillation of a disturbance that gives rise to a wave.

(a)

By redrawing the diagram in the spaces below, add arrows to show the direction of wave energy transfer to illustrate the difference between

(i)

a transverse wave and 

(1) (ii)

a longitudinal wave.

(1)

A wave travels along a stretched string. The diagram below shows the variation with distance along the string of the displacement of the string at a particular instant in time. A small marker is attached to the string at the point labelled M. The undisturbed position of the string is shown as a dotted line. Directions of wave travel

M

(b)

On the diagram above (i)

draw an arrow to indicate the direction in which the marker is moving. (1)

(ii)

indicate, with the letter A, the amplitude of the wave. (1)

(iii)

indicate, with the letter  λ, the wavelength of the wave. (1)

(iv)

draw the displacement of the string a time

T  4

later, where T is the period of oscillation of the wave. Indicate,

with the letter N, the new position of the marker. (2)

8

 –1 The wavelength of the wave is 5.0 cm and its speed is 10 cm s . (c)

Determine (i)

the frequency of the wave. ........................................................................................................................... ...........................................................................................................................

(ii)

how far the wave has moved in

T  4

(1)

s.

...........................................................................................................................

...........................................................................................................................

(2) Interference of waves (d)

By reference to the principle of superposition, explain what is meant by constructive interference. ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... (4) (Total 14 marks)

6.

This question is about waves and wave motion. (a)

Describe, by reference to the propagation of energy, what is meant by a transverse wave. Transverse wave (2) ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................

(b)

State one example, other than a wave on a string, of a transverse wave. ..................................................................................................................................... (1)

9

A transverse wave is travelling along a string that is under tension. The diagram below shows the displacement of part of the string at time t = 0. The dotted line shows the position of the string when there is no wave travelling along it. displacement / cm

5.0

(c)

15

25

35

distance along string / cm 45

On the diagram above, draw lines to identify for this wave (i)

the amplitude (label this A); (1)

(ii)

the wavelength (label this  λ).

(1) (d)

 –3  –1 The period of the wave is 1.2 × 10 s. Deduce that the speed of the wave is 250 m s . ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... ..................................................................................................................................... .....................................................................................................................................

(2) (e)

 –4 Using the axes below, draw the displacement of the string when t = 3.0 × 10 s. (The displacement of the string at t = 0 is shown as a dotted line.)

displacement / cm

5.0

15

25

35

distance along string / cm 45

(3) (Total 10 marks)

10

7.

The properties of sound waves Reflection and Refraction One method of finding the position of fish beneath a boat is to send out a pulse of sound waves from the bottom of a boat and   –1 time how long the pulse takes to return as shown below. The speed of sound waves in water is 1500 m s .

water  emitter and receiver 

fish

(a)

The time between the pulse leaving the emitter and returning to the receiver is 12 ms. Calculate the distance from the  bottom of the boat to the fish. ................................................................................................................................... ................................................................................................................................... ...................................................................................................................................

(2) In order to find fish using this method, the effects of diffraction at the fish need to be minimized. (b)

(i)

The diagram below shows plane wavefronts incident on an obstacle. Complete the diagram to show what is meant by diffraction of the wavefronts. direction of  movement of  wavefronts

(2)

(ii)

Explain why you would expect the effects of diffraction to be negligible when sound of frequency 60 kHz is incident on a large fish. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... .........................................................................................................................

(2) The Doppler effect can be used to determine the speed of an object. (c)

(i)

Explain what is meant by the Doppler effect . ......................................................................................................................... ......................................................................................................................... .........................................................................................................................

(2)

11

(ii)

A train approaches and then passes by a stationary observer. The train is moving with constant velocity and emits a sound of constant frequency. The observer hears the frequency change from 490 Hz to 410 Hz. The speed of   –1 sound in air is 340 m s . Estimate the speed of the train. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (4) (Total 12 marks)

8.

Waves (a)

Distinguish, in terms of the propagation of energy, the difference between a transverse travelling wave and a longitudinal  travelling wave. ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... ................................................................................................................................... (3)

(b)

The diagram below shows an aluminium rod AB of length 1.50 m hanging horizontally from two strings.

string

string

A

B aluminium rod  1.50 m

hammer 

End A of the rod is hit gently with a hammer. As a result, a wave pulse travels down the rod and is reflected from end B. The hammer remains in contact with the rod until the pulse reflected from end B reaches A. This pulse causes the hammer to rebound from the end of the rod.

(i)

Suggest, giving a reason , whether the wave pulse is longitudinal or transverse. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2)

12

(ii)

 –4 The hammer is in contact with end A of the rod for 6.00  10 s. Calculate the speed of the pulse in the rod. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (2)

(iii)

As a result of the rod being hit with the hammer, a sound is heard. Suggest how this sound arises. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3)

(Total 10 marks) 9.

Travelling waves (a)

Graph 1 below shows the variation with time t of the displacement d of a travelling (progressive) wave. Graph 2 shows the variation with distance x along the same wave of its displacement d .

4 Graph 1 d / mm 2 0

0.0

0.1

0.2

0.3

0.4

0.5

0.6 t / s

0.0

0.4

0.8

1.2

1.6

2.0

2.4

 –2  –4

Graph 2 d / mm

4 2 0

 –2

 x

/ cm

 –4

(i)

State what is meant by a travelling wave. ......................................................................................................................... .........................................................................................................................

(1)

13

(ii)

Use the graphs to determine the amplitude, wavelength, frequency and speed of the wave. Amplitude:

................................................................................................. (1)

Wavelength:

................................................................................................. (1)

Frequency:

................................................................................................. ................................................................................................. (1)

Speed: ................................................................................................. ................................................................................................. (1) Refraction of waves (b)

The diagram below shows plane wavefronts incident on a boundary between two media A and B.

medium A medium B

The ratio

refractive index of  medium B refractive index of  medium A

is 1.4.

The angle between an incident wavefront and the normal to the boundary is 50 . (i)

Calculate the angle between a refracted wavefront and the normal to the boundary. ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... ......................................................................................................................... (3)

(ii)

On the diagram above, construct three wavefronts to show the refraction of the wave at the boundary. (3) (Total 11 marks)

14

MARK SCHEME! 1.

(a)

(b)

ray: direction in which wave (energy) is travelling; wavefront: line joining (neighbouring) points that have the same phase / displacement / Or suitable reference to Huygen’s principle; ray is normal to a wavefront;

3

(i)

wavefront parallel to D;

1

(ii)

frequency is constant; since v = f  λ, v   λ; wavelength larger in medium I, hence higher speed in medium I;

3

 Allow solution based on angles marked on diagram or speed of wavefronts.

(iii)

ratio =

=

(c)

(i)

(ii)

3.0 1.5

v I  v R

(iv)

  I    R

(or based on Snell’s law);

= 2.0 allow   0.5;

2

velocity / displacement / direction in (+) and (–) directions; idea of periodicity;

2

period = 3.0 ms; frequency =

(iii)



1 T 

= 330 Hz;

2

 Accept any one of the following. at time t = 0, 1.5 ms, 3.0 ms, 4.5 ms, etc;

area of half-loop = 140  10 squares  –3 = 140 × 0.4 × 0.1 × 10  –3 = 5.6 × 10 m

1

 –1 / mean v = 4.0 m s accept   0.2;  –3 / 4.0 × 1.5 × 10 ;  –3 / 6.0 × 10 m;

2

 Award  [1]  for area of triangle.

(v)

(twice) the amplitude;

1

 Allow distance moved in 1.5 m s.

[17]

2.

(a)

longitudinal;

1

(b)

(i)

wavelength = 0.5 m;

1

(ii)

amplitude = 0.5 mm;

1

(iii)

correct substitution into speed = frequency × wavelength;  –1 to give v = 660 × 0.5 = 330 m s ;

2 max

[5]

15

3.

(a)

(b)

(i)

distance travelled per unit time;  by the energy of the wave / by a wavefront;

2

(ii)

velocity has direction; but light travels in all directions;

2

(i)

distance in a particular direction; (accept in terms of energy transfer) (of a particle) from its mean position;

2

(ii)

(c)

longitudinal : displacement along; transverse: displacement normal to; direction of transfer of wave energy / propagation, not motion;  Award  [0] for left / right and up / down for longitudinal / transverse .

3

(i)

 700      75  

 –1 = 9.3 km s ; (±0.1)

1

(ii)

 700     120 

 –1 = 5.8 km s ; (±0.1)

1

 Award  [1 max] if the answers to (i) and (ii) are given in reversed order.

(d)

(i)

P shown as the earlier (left hand) pulse;

1

(ii)

laboratory L3;

1

(iii)

eg pulses arrive sooner; smaller S-P interval; larger amplitude of pulses;

3

 Allow any feasible piece of evidence, award  [1] for each up to [3 max] .

(iv)

distance from L1 = 1060 km; ( 20) distance from L2 = 650 km; ( 20) distance from L3 = 420 km; ( 20)  Accept 3 significant digits in all three estimates. some explanation of working;

(v)

position marked, consistent with answers to (iv); to the right of line L2 L3, closer to L3;

4

1 max

 If the answers given in (iv) means that the point cannot be plotted, then only allow the mark if the candidate states that the position cannot be plotted / does not make sense.

(e)

(i)

illustration showing node at centre, antinode at each end;

(ii)

wavelength of standing wave = (2 × 280) = 560 m / ecf   or

3.4  10 3 6

frequency =

1

= 570 m;

(3.4  10 3 ) 560

 6Hz

 or wavelength of standing wave = (2 × 280) = 560 m;

earthquake frequency is natural frequency of vibration of   building / mention of resonance / multiple / submultiple if ecf;

3

[25]

16

4.

(a)

the net displacement of the medium / particles (through which waves travel); is equal to the sum of individual displacements (produced by each wave);

2 max

 Award a good understanding  [2 max] and a reasonable one [1 max] .

(b)

Wave X and wave Y should be identical.

X and Y

A

B

correct phase for wave X; correct phase for wave Y; amplitudes the same for each wave; amplitude for each wave is two divisions;

(c)

(i)

the phase difference between light leaving S 1 and S 2 is constant;

4 max

1

 Do not penalize the candidate if they state “has the same phase”.

(ii)

to produce sufficient diffraction; for the beams to overlap; OWTTE ;

2 max

[9] 5.

Wave properties (a)

(i)

1

(ii) 1

(b)

A M

 N

(i)

downwards;

1

(ii)

correct marking of A;

1

(iii)

correct marking of  ;

1

(iv)

+ve sine curve; correct position of N;

2

Watch for ecf from (i). 17

(c)

v

(i)

 f =

(ii)

T = 0.5 s;

to give 2.0 Hz;

 

 s =

vT  4

1

= 1.25 (1.3) cm;

 or

in

=

(d)

T  4 5 4

wave moves forward 

1 4

  ;

= 1.25 (1.3) cm;

2 max

 Principle of  superposition: when two or more waves overlap, the resultant displacement at any point; is the sum of the displacements due to each wave separately / OWTTE ;  Award  [2 max] for an answer that shows a clear understanding of the principle, [1] for a reasonable understanding and  [0] for a weak answer.  Explanation:

= suitable diagram; when two +ve pulses (or two wave crests) overlap, they reinforce / OWTTE;

4

 Any situation where resultant displacement looks as though it is th e sum of the individual  displacements. Mark the description of the principle and the description of constructive interference together.

[14]

6.

(a)

a wave in which the direction of energy propagation; is at right angles to the direction of vibration of the particles of the medium through which the wave is travelling / OWTTE ;

2

 or

 suitable labelled diagram eg 

vibration of   particles / medium

(b)

any em wave / elastic waves in solids / accept water;

direction of  energy propagation

1

18

(c)

displacement / cm

A

5.0

15

25

35

45

distance along string / cm

correct annotation

(d)

(i)

A (4.0 cm);

1

(ii)

 λ

(30.0 cm);

1

 f =

1 T 



1 1.2  10 3

= 830 Hz;

 –1 c = f  λ = 830 × 0.30 = 250 m s ;

2

(e)

displacement / cm

5.0

15

25

35

45

distance along string / cm

troughs / peaks moved to the right;  by  λ / 4 (7.5 cm); (judge by eye) wave continuous between x = 0 and  x = 45 cm;

3

[10]

19

7.

The properties of sound waves (a)

(b)

substitution into speed = distance / time to get distance =1500  0.012 = 18m; therefore, depth = 18  2 = 9m;

(i) (ii)

appropriate wavefronts shown in geometric shadow region; of constant wavelength;

(i)

(ii)

2

substitution of correct values into v = f  to get  = 0.025m; so obstacle (fish) significantly larger than wavelength hence diffraction effect small / OWTTE ; or the wavelength is very small; so diffraction will be small for any reasonably sized fish;

(c)

2

change in received frequency of sound (wave); as a result of relative motion of source and observer;  Accept other general descriptions but award  [1 max] for an answer  that just gives an example of the Doppler effect.

1

340

 f  ; v

410 

1

410

2

 f  ; v

490 

490

2



340

340  v 340  v

;

1

to get v = 30ms

;

or:

490 

 f  ; v

1

340

with f = 450Hz;  justification of  f = 450Hz;

1

to get v = 28ms

;

or:

410 

 f  ; v

1

340

with f = 450Hz;  justification of  f = 450Hz;

1

to get v = 33ms

;

4

[12]

20

8.

Waves (a)

the direction in which energy (of the wave) is propagated; for a transverse wave it is at right angles to the direction of vibration of the particles (of the medium through which the wave is travelling); for a longitudinal wave the direction of energy propagation is in the same direction as the vibration of the particles;

3

Accept answers based on diagrams for full marks provided direction of  energy transfer and direction of oscillation are clear on the diagram. (b)

(i)

longitudinal; it is likely that the hammer will set the atoms of the rod to vibrate in the same direction as the direction of the motion of the hammer  / OWTTE ;  Award  [0] if no explanation or poor explanation.

2

Or

hammer would not experience a rebounding force (if wave were not longitudinal) / OWTTE; some reference to direction of propagation of energy being along the length of the rod; (ii)

 s = 3.00m;

3.00  s v   5.00 10 3 ms 1 ; 4 t  6.00 10

2

Watch out for incorrect answers based on v = f   and 

 f  

1 6 10 4

1667

Hz ! It can give the correct numerical result 

with a completely wrong argument.

(iii)

the hammer blow / pulse sets the rod vibrating; the vibration of the rod causes the air molecules in contact with the rod to vibrate; thereby setting up a longitudinal wave in the air / creates the sound  / OWTTE ;

3

[10] 9.

Wave phenomena (a)

(i)

wave that transfers energy;

1

(ii)

amplitude

= 4.0mm;

1

wavelength

= 2.4cm;

1

frequency

=

1 0.3

;

= 3.3Hz; = 3.3  2.4;

speed

= 8.0cms

(b)

(i)

1

1

;

1

angle of incidence = 40;

sin r 

sin 40 1 .4

r = 27; angle = 63;

3

 Award  [1 max] for angle of incidence = 50    , r = 33  . (ii)

construction: wavefronts equally spaced; separation less in medium B; angle in medium B correct  by eye;

3

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