1 Wave Anatomy & Wave Speed

Becky McCoy

Lesson Title: Wave Anatomy & Equations

Timing: 60 minutes

Target Audience: 11th and 12th grade Physics Class

Objectives: Students Will Be Able To: • Describe parts of a wave • Determine the difference between longitudinal and transverse waves • Perform calculations to determine wavelength, velocity, and frequency The Teacher Will Be Able To: • Assess student understanding of waves • Give students opportunities to observe and describe wave phenomena • Allow students to verbalize knowledge of waves in small and large groups

Standards Assessed: New York State Standards in Physics Physical Setting Indicator 4.3: Students can explain variations in wavelength and frequency in terms of the source of the vibrations that produce them, e.g., molecules, electrons, and nuclear particles. 4.3a An oscillating system produces waves. The nature of the system determines the type of wave produced. 4.3b Waves carry energy and information without transferring mass. This energy may be carried by pulses or periodic waves. 4.3c The model of a wave incorporates the characteristics of amplitude, wavelength,* frequency*, period*, wave speed*, and phase. 4.3dMechanical waves require a material medium through which to travel. 4.3e Waves are categorized by the direction in which particles in a medium vibrate about an equilibrium position relative to the direction of propagation of the wave, such as transverse and longitudinal waves.

Misconception(s) Addressed: • • • • • •

All waves travel the same way. Light is one or the other--a particle or a wave--only. Light can be a particle at one point in time and a wave at another point in time. Particles can't have wave properties. Waves can't have particle properties. The position of a particle always can be exactly known.

Becky McCoy

Prior Knowledge: Mechanics, Kinematics, Circular Motion, and Pendulum Units. Introductory lesson on waves. Aim: Define a wave by its anatomy and velocity equation. Concept Map Vocabulary: • • •

Amplitude Crest Trough

• • •

Wavelength Period Frequency

Necessary Preparation: COPIES • Wave Worksheet (not associated with this lesson) • Practice Problem Sheet MATERIALS • Chart paper • Markers SET UP

•

Wave Speed

Becky McCoy

Lesson Plan

Aim: Define a wave by its anatomy and velocity equation. Physics Push-Up: KWL Chart (10 minutes) As students walk in, have them fill out the rubric from the Pendulum Unit Project and submit their projects. Have students work in small groups to develop a KWL chart regarding waves on chart paper. These should be hung around the classroom if possible.

Activity: Wave Anatomy & Equation (20 minutes) Materials: • • •

Wave Unit sheet Computer and projector or SMARTboard Practice Problem Copies

Procedure: Last class, the concept of waves was introduced considering that a transverse wave has the same shape as the graph of the periodic motion of a simple harmonic oscillator over time. Think-Pair-Share: What is a wave? The transmission of energy through a medium. “We discussed two types of waves – Transverse and Longitudinal – and they’re anatomy. Today we’re going to look at them more closely.” A quick reminder of the difference between the two waves: A Band: http://www.youtube.com/watch?v=fk9vGmpqlis E Band: http://www.youtube.com/watch?v=rTcHqbIQbX8 Another look at waves: Transverse: http://www.youtube.com/watch?v=g49mahYeNgc Longitudinal: http://www.youtube.com/watch?v=XA5XW0sGN_I Draw diagrams of the two waves near each other and have students label the wavelength, period, direction of velocity, displacement of the particle within the medium, the crest, trough, amplitude, etc. and introduce compression and rarefaction within the longitudinal wave (comparable to the crest and trough in the transverse wave). Ask students which equation we usually use for velocity: v

= d/t

“How might we develop this equation to describe the velocity of a wave?” Since velocity is measured in meters-per-second, we want the units to end up that way as well.

Becky McCoy

This means: v

=λ f

Practice problem together: Dong-Won and Phil are on a dock at a lake. They are counting waves that are passing by. a) In 45 seconds, 15 waves pass by them. What is the frequency of these waves? When is the period? b) If each wave is 0.8 meters long, what is the velocity of the waves? a) f = waves/second = 45/15 seconds = 3 /sec T = seconds/wave = 15/45 = 1/3 sec b) v = λ f = (.8)(3) = 2.4 m/s

Activity Summary: Practice Problems (20 minutes) Have each lab group work together to solve a velocity equation problem from the problems listed below. Each team should have a few minutes to solve their problem and then present their process and answer on the board for the rest of the class.

Homework: Complete Practice Problems (5 minutes) Students should complete the practice problem sheet used in the activity summary.

Exit Strategy: Exit Slip (5 minutes) On a scrap piece of paper, students should draw a transverse and a longitudinal wave with a wavelength of 1 m and period of 4 seconds. Then students should solve for the velocity of the wave. Students should also add anything to any column of their KWL chart if needed.

Extension Activity: Give students the opportunity to work on the homework.

Assessment: Formative: • Student KWL Charts • Student conversations and contributions to discussion Summative: • Homework responses

Resources: Transverse Wave: http://www.youtube.com/watch?v=g49mahYeNgc Longitudinal Wave: http://www.youtube.com/watch?v=XA5XW0sGN_I Mike Shum’s “Waves and Wave Motion” worksheet Faughn, J. S., & Serway, R. A. (2003). College Physics (6 ed.). New York: Brooks Cole.

Becky McCoy

Notes & Adaptations:

Becky McCoy

Practice Problems for Waves 1. A bat can detect small objects such as an insect whose size is approximately equal to one wavelength of the sound the bat makes. If bats emit a chirp at a frequency of 60.0Hz and if the speed of sound in air is 340 m/s, what is the smallest insect a bat can detect? 2. If the frequency of oscillation of the wave emitted by an FM radio station is 88.0 MHz, determine the waves (a) period of vibration and (b) wavelength. (Radio waves travel at the speed of light, 3.00 x 108 m/s). 3. A piano emits sound waves with frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths spanned by this instrument. The speed of sound in air is approximately 343 m/s. 4. A transverse wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 seconds. Also, a given maximum travels 425 cm along the rope in 10.0 seconds. What is the wavelength? 5. Ocean waves are traveling to the east at 4.0 m/s with a distance of 20 m between crests. With what frequency do the waves hit the front of a boat when the boat is at anchor? 6. A girl on the beach watching water waves sees 4 waves pass by in 2 seconds, each with a wavelength of 0.5 m. Find (a) the period and frequency of the wave and (b) the speed of the wave. 7. If a wave has frequency 1014 Hz and speed v = 100 m/s, what is its wavelength? How will the wavelength change if the frequency is 1015 Hz? 8. A phone cord is 4.00 m long. Plucking one end of the taut cord produces a transverse wave. The pulse makes four trips down and back along the cord in 0.800 seconds. What is the wave’s velocity? 9. A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes the wave 0.800 seconds to reach the opposite tower, 20.0 m away. What is the velocity of the wave? 10. A wave pulse travels the length of a slinky in 0.1 seconds. If the slinky is 3.0 meters long, find the speed of the wave.