PHYS_EX7

Experiment 7: Velocity of Sound Laboratory Report Dana Young, Dana Yu, Ray Allen Zafra*, Lloyd Pineda Department of Math and Physics College of Science, University of Santo Tomas España, Manila Philippines

Sound

Abstract The velocity of experiment

was

sound in

determined

by

this three

activities: air column resonation, speed of sound and speed of sound in a solid. In the air column resonation activity, the students computed the aerial speed of sound bu utilizing the formula V = 331+0.6t where t refers to the temperature. Second is through the use of a computer, the group calculated the speed of sound through the division of the tube length by ½ of the time interval. Finally, the theoretical speed of sound in solid was computed by VR= square root of Y/p where Y is the Young's modulus and p is the density of the rod. Subsequently, the percent error was computed and obtained from the three activities.

is

defined

as

a

mechanical, longitudinal wave made through

object

vibration

from

equilibrium that promulgates through a certain medium, be it solid, liquid or even gas, from one location to another. Specific and certain factors compose sound. The speed of sound pertains to the speed at which sound waves propagate and traverse through materials.

On

the

other

hand,

wavelength (λ) refers to the overall distance

between

the

adjacent

maxima/crest and minima/trough. Frequency is then defined as the number of cycles per unit time while resonance is the tendency of one system to fluctuate with greater amplitude at some frequencies than at others.

1. Introduction

change when reflected from a fixed end. Longitudinal waves are those wherein the

2. Theory

particle motions are made of the fluctuations Sound is considered a wave, both in the mechanical and longitudinal nature. Vibration is a way in which sound is

with reference to the promulgation direction. Means of air propagation is associated with this wave.

produced. When a vibration disturbs a particle in a medium, it therefore affects the

Speed of sound is different from each

other particles, thus creating a wave pattern.

medium. Sound travels better and faster

Frequency, wavelength amplitude, crest, and

though solid than in air. Because sound is

troughs are the different parts of a wave.

considered as vibrations that pass from one

Frequency, as mentioned, is defined as cycles

particle to another, the more compact the

per second. Wavelength is the overall

particles, the faster is sound travel. This

distance between two adjacent crests, troughs

explains why sound travels faster in solid

and/or cycles. The maximum positive

than in liquid, since the molecules in solid are

displacement is the amplitude. Crests and

more compactly bonded compared to those in

trough are respectively the highest and lowest

liquid. The same scenario can be observed

points of a wave cycle. V=fλ is the basic

and said respectively for liquid and gas.

equation which depicts mathematically the

Vacuum environment does not promote

relationship of the variables of a wave

sound travel. Medium elasticity and density

motion.

are also considered in wave speed.

Different

waves

are

produced In activity 1, the following equations

depending on the medium type. Standing waves are produced through air column

were used:

vibrations while longitudinal waves are made from rod vibrations. Standing waves are 𝜆 = 4𝐿 + 0.3𝐷

associated with resonance and it is thus the

𝑉𝐸 = 𝑓𝜆

principle behind the sound produced by instruments, specifically wind instruments. It

𝑉𝑇 = 331 + 0.6𝑡

came from a combination of reflection and inference using the wave property of phase

Where:

λ= wavelength of the sound produced L= distance between the top of the glass tube

λ= twice the average distances of two consecutive displacement nodes

and point with the loudest sound

VR= speed of sound in the rod

D= diameter of the resonance tube

λR= is the wavelength of the sound in the rod

VE= experimental speed Percent error was calculated in all the

VT= theoretical speed

activities using the equation T= temperature %𝑒𝑟𝑟𝑜𝑟 the following equations were used for

=

|𝑇𝑟𝑢𝑒 𝑣𝑎𝑙𝑢𝑒 − 𝐸𝑥𝑝𝑒𝑟𝑖𝑚𝑒𝑛𝑡𝑎𝑙 𝑣𝑎𝑙𝑢𝑒| 𝑥100 𝑇𝑟𝑢𝑒 𝑉𝑎𝑙𝑢𝑒

activity 2: 𝐿 0.5𝑇

𝑉= V= speed of the sound L= length of the tube T= time interval

3. Methodology Activity 1: Resonating Air Column

Activity

3

used

the

following

equations:

Begin with the water on top of the resonance tube and then strike a tuning fork

𝑓=

𝑉 𝜆

𝑉𝑅 = 𝑓𝜆𝑅

with a mallet. Place the vibrating tuning fork over the glass tube. Lower the vessel until the loudest sound is heard. Determine and mark the point where the sound was heard. If the aforementioned procedures yielded no result,

Where: f= frequency of the of the sound produces

strike the fork again. Record it as L. Convert distance to meters. Measure the diameter of the resonance tube. Compute the wavelength

V= theoretical value of the speed in air

of sound produced.

= 4L + 0.3D

f = V/

V=f

VR = f R

V= 331 = 0.6t

VR √(Y/p)

Activity 2: Speed of Sound

4. Results and Discussion

Connect the Vernier microphone to the interface. Position the microphone near the open end of the closed tube. Utilizing the computer program, snap your fingers or clap

Activity 1: Resonating Air Column Temperature of air = 17°C Diameter of Resonance Tube = 0.035 m

once the data collection starts. From the graph displayed, determine the time interval

Table 1.1: Summary of values obtained for

between the start of the first vibration and the

the resonating air column

beginning of the echo vibration. Compute for

Frequency

the speed of sound by diving the length of the

of tuning

tube by ½ of the time interval obtained.

Fork

Compute for the % error with the same

Wavelength (m) Trial 1

Trial 2

Trial 3

0.101

0.149

0.114m

m

m

0.4145

0.6065

0.4665

m

m

m

341.3 1/s

accepted value used in the previous activity.

Activity 3: Speed of Sound in Solid Place a thin layer of cork dust inside the Kundt’s tube. Clamp the rod at its center and rub the rod with a piece of cloth with

Table 1.2: Summary of the computed values for the resonating air column

powder of coarse nature. This will vibrate the rod, producing a sound of high frequency. A

Average

Experim

standing wave patter will be thus formed in

Wave-

en-tal

ti-cal

erro

the cork dust inside the tube. Measure the

length

speed

speed

r

341

0.121

displacement nodes. Get the average of the

.3

m

distances. Determine the frequency of sound

1/s

distances

between

two

consecutive

produced using the formula. Compute the % error.

Theore %

04958

169.22

341.2

50

The speed was computed in the

m

m/s

m/s

%

experiment which represented the velocity of sound. The velocity of sound, defined as the

In Activity 1, the wavelength of the

sound that travels in a medium may be found

sound was determined through the utilization

if the frequency and the wavelength are thus

of two frequencies of tuning forks, 341.3 1/s

known. The relationship between these

and an unknown frequency though the use of

quantities is:

the resonance of an air column. The time

v = fλ

allotted, coupled with the crowding resulted where:

in our inability to complete the activity. The material used in the experiment

V=velocity of sound propagation

was a long cylindrical tube water container

f=frequency

attached to a reservoir with a tuning fork. The

λ = wavelength

length of the water may be altered by

Referring to table 1.1, the higher the

elevating or lowering the water level while

frequency, the lower the wavelength. On the

the tuning fork is held over the open end of

other hand, based on table 1.2, the higher the

the tube. Resonance is then exhibited through

frequency, the lower the speed and/or

the loudest sound produced while the tuning

velocity.

fork is held over the cylinder’s top. In other words, resonance is indicated by the sudden increase in the intensity of sound when a column is adjusted and positioned to the

Activity 2: Speed of Sound Length of tube: 0.44 m

certain and proper length Table 2: Summary of values obtained for the The water surface formed a standing

speed of sound

wave node since the air was constricted and was not free to move longitudinally. The

Trial

Total Travel Time

open end provided the conditions for an antinode, but the actual had been found to

1

0.0026 s

occur outside the tube.

2

0.0026 s

Average

0.0026s

Experimental speed

338.46 m/s

Theoretical speed

341.2 m/s

% error

0.8 %

Activity 3: Speed of Sound in Solid

Sound promulgates hastily in solid medium. The concept behind the fact is because of the tighter bond of molecules in solid molecules ac compared to liquid and gas. Due to this, it requires less time for the vibration to travel in a solid medium than in

The speed of sound, as earlier

a medium of liquid or gaseous nature.

mentioned is defined as the overall distance travelled per unit time by a specific sound wave through an elastic medium. In Activity 2, a Vernier microphone was connected to the interface and was placed near the open end of the closed tube. When the set up was established, one of the members was asked to snap or clap near the tube to produce a graph in the computer. As research shows, sound pressure is the difference between an instantaneous pressure given a point where in a sound wave and the pressure of a medium is utmost present. Sound pressure decreases inversely in proportion to the distance. Trial 1 yielded a travel time of 0.0026s and trial 2 yielded the same value. The speed of sound determined was 444.53m/s. The percent error yielded 0.8 %by using the formula theoretical yield-experimental yield/theoretical yield, where in the theoretical speed found was 341.2 m/s.

In a Kundt’s tube set up, sound transmission was through either longitudinal or transverse waves. The vibration was then produced on the clamp rather than the disk as it has the ability to damage or even break the glass tube. Standing waves were then produced when the rod was correctly stroked into a vibrating state. The wavelength was twice as the length of the rod. The nodes and antinodes transmitted through the air column was physically visible due to the cork dust inside. Pulling on the rod with a powdered cloth without pulling the cloth entirely off the rod resulted in a longitudinal vibration as well as a sound of high frequency. Dust heaps appeared

separately

after

continuous

stroking. The distance between the two consecutive dust heaps was subsequently measured determined.

and

then

the

average

was

Table 3 displays the measured and computed

constraints and crowding over the work

properties of a wave. The computed speed

stations, we were only able to achieve half of

generated an experimental speed of 4881.87

the activity. For the speed of sound in air

m/s and a theoretical speed of 5091. 75 m/s,

resulted to an experimental speed of 169.22

higher than those computed from the

m/s and a theoretical speed of 341.2 m/s, and

preceding two activities. This only shows that

resulted to a percent error of 50%. For the

that the velocity of sound is definitely higher

speed of sound, the second activity, using the

in a solid medium. There was a 4.12 % error

computer, the speed of sound determined was

computed with reference to 5000m/s as an

an experimental speed of 338.46 m/s and a

accepted value.

theoretical speed of 341.2 m/s and then, the

Table 3. Variables of the speed of sound in

percent error found was 0.8%. As for the final activity, the class computed for both the

solid

theoretical speed and percent error for Average of distances 0.0643 m

sound’s speed in a solid medium and the

between node t node

resulting values were respectively 5091 m/s

Wavelength of sound 0.1286 m

and 4.12%,. With these results generated

in air

from the experiment, I conclude that the class

Frequency of sound

2653.19 1/s

was able to attain all the objectives in the said

Length of rod

0.46 m

experiment.

Wavelength of sound 1.84 m in rod Experimental

6. Applications speed 4881.87 m/s

of sound in the rod

1. What is the relation between the

Theoretical speed of 5091 m/s

frequency and wavelength of sound

sound in the rod

produced in a medium?

% error

4.12 % The relationship

5. Conclusion

between sound

frequency and wavelength is inversely proportional. Velocity stays constant, If one

For the first activity, two trials were supposed to be made but due to time

increases the frequency, the wavelength shows a decrease and vice versa.

2. What is the use of water in Activity 1?

average. What frequency would be most effectively detected by the ear at 30°c? V= 331+0.6 (30°c)

Water’s purpose in Activity 1 is

V= 349 m/s

explained in the “ocean wave theory”. Since

λ= 4(0.027 m) + 0.3(0.007 m)

water was used as the medium for this

λ= 0.1101 m

activity, the surface of the water constitutes

f = 349/ 0.1101

the standing wave node due to air’s inability to move longitudinally. In addition, and as mentioned, sound is a longitudinal wave and therefore fluctuates in a medium.

f = 3169.85 /s 5. Suppose that we increase the temperature of the air through which a sound wave is traveling. a) what does this have on the velocity

of

the

wave?

Explain

3. In medical practice, ultrasound in the range of 1 to 5 megahertz is being used as an imaging modality. The associated

a.) Speed of sound in air is attainable through

wavelengths in a typical human tissue organ

the equation: v_ (sound at t)=331 m/s+0.6 t.

range from 0.3mm to 0.06mm. Find the

As the temperature increases, the speed of

velocity of ultrasound in the tissue.

sound increases as well. b.) Sound wavelength is given by the

This aforementioned piece of technology is a method that allows the determination of sound within living tissues through the utilization of reflecting and acoustic sensors.

equation: λ =ν/f. As stated in the previous problem, the speed of sound in air increases as the temperature of air increases; it can be deduced that as air temperature increases,

Frequency = 5 megaHZ = 5 x 106 Hz Wavelength = 0.3 mm = 3 x 10-4 m

wavelength increases as well. 6. If you were lying on the ground, would you

Velocity = Frequency x Wavelength Velocity = 5 x 106 Hz x 3 x 10-4 m Velocity = 1500 m/s 4. The outer ear of a human may be thought of as a closed pipe 2.7 cm long on the

hear footsteps sooner or later with your ear touching the ground or not? Due undoubtedly

to

the

travels

fact

that

quicker

sounds in

solid

mediums, one can hear sound sooner as the ear touches the ground.

References [1] The Wave Equation. (2016). Retrieved from http://www.physicsclassroom.com/cl ass/waves/Lesson-2/The-WaveEquation [2] Nave, R. (2012). Wave Speeds. Retrieved

from

http://hyperphysics.phyastr.gsu.edu/hbase/Sound/souspe2.ht ml [3] Resonance Tube: Velocity of Sound. (n.d.) Retrieved from http://hyperphysics.phyastr.gsu.edu/hbase/Class/PhSciLab/re stube2.html [4] The Speed of Sound in Other Material. (n.d.). Retrieved from https://www.ndeed.org/EducationResources/HighSch ool/Sound/speedinmaterials.htm