Unit 7 - Wave and Energy Transfer

Equations Variables, Units

Conversion of Intensity to Decibel LevelIntensity (W/m2) Decibel level Examples1 x 10-12 0 threshold of hearing 1 x 10-11 10 rustling leaves1 x 10-10 20 quiet whisper1 x 10-9 30 whisper1 x 10-8 40 mosquito buzzing1 x 10-7 50 normal conversation1 x 10-6 60 air conditioning at 6 m1 x 10-5 70 vacuum cleaner1 x 10-4 80 busy traffic, alarm clock1 x 10-3 90 lawn mower1 x 10-2 100 subway, power motor1 x 10-1 110 loud rock concert1 x 100 120 threshold of pain1 x 101 130 thunderclap, machine

1 x 103 150nearby jet

airplane

Speed of Sound at 20 o C Material Speed (m/s)Air 343Air (0o C) 331Helium 1005Hydrogen 1300Water 1440Sea Water 1560Iron and Steel 5000Glass 4500Aluminum 5100

Unit 7 Objectives: Waves and Sound

By the time we finish this unit and all related activities you should be able to:

1. Define simple harmonic motion.

2. Relate the period of a pendulum and a spring to the frequency.

3. Describe the characteristics and properties of waves. A) Define and identify the crest, trough, amplitude, and wavelength on a

transverse wave. B) Define and identify compressions, rarefactions, and wavelength on a

longitudinal wave.

4. Identify waves as a transfer of energy, not matter, and describe the factors that affect the speed of a wave.

5. Compare and contrast a wave pulse, a transverse wave, and a longitudinal wave.

6. Relate the wave speed, wavelength, and frequency; solve problems using these quantities.

7. Describe what happens as a wave reaches a fixed or free boundary, and be able to apply the principle of superposition when waves interfere.

8. Use the principle of superposition to describe resonance and standing waves. A) Distinguish between nodes and antinodes and what causes them.B) Solve problems using the wave equation for standing waves.

9. Understand the properties of sound such as pitch, intensity, and how it is transmitted.

10. Define the Doppler shift and identify some of its applications.

11. Use the principle of superposition to describe interference of sound waves, beats, and timbre.

Worksheet 1 - Wave PropertiesMultiple Choice.1. A (An) _______ transmits energy without transferring matter.A) light particle B) sound wave C) electron D) proton

2. Waves on a banjo string are _________ waves.A) transverse B) electromagnetic C) longitudinal

D) surface

3. The shortest time interval during which wave motion repeats is theA) amplitude. B) period. C) frequency.

D) wavelength.

4. The number of complete vibrations per second is the A) amplitude. B) period. C) frequency.

D) wavelength.

5. The shortest distance between two points on a wave where the wave is repeated is theA) amplitude. B) period. C) frequency.

D) wavelength.

6. The greatest displacement from the equilibrium position is called theA) amplitude. B) period. C) frequency.

D) wavelength.

7. The speed of any mechanical wave depends on theA) medium through which it travels. B) amplitude. C) frequency

D) wavelength.

Problems8. A wave generator produces 16 vibrations in 2.0 seconds. A) What is the frequency? B) What is the period? C) If the wavelength of the waves produced is 3.5 meters, what is the speed of the waves?

9. A wave on Utah Lake passes by two docks that are 40.0 m apart.A) If there is a crest at each dock and another three crests between the two docks, determine the wavelength. B) If 10 waves pass one dock every 16 seconds, determine the period and frequency of the wave.

10. The velocity of waves in a spring is 10 m/s. If we pull the spring tighter, will it have an effect on the velocity? Explain.

11. On the waves below, label the wavelength, crest, trough, compression, rarefaction, and amplitude of the wave.

Sine Wave

Worksheet 2- Wave Equation

1. If a wave vibrates back and forth three times each second, and its wavelength is 2 meters, A) what is its frequency? B) What is its period? C) What is its speed?

2. When your aunt Marge jumps in the pool, water waves are sent out with a wavelength of 50 cm. Being bored of sunbathing, you count 5 waves splashing you every 10 seconds. What is the speed of the water waves?

3. Playing with your rubber ducky in your tub, you dunk him once them watch him bob up and down 2 times every second. A) What is the period of his bobbing? B) What is the frequency of his bobbing? C) If he sends out 2 cm long waves, what is the speed of the water waves?

4. Without any friends to play jump-rope with, you decide to use it to shake it up and down to make waves. You lift it up 2 cm, then back to equilibrium, then down 2 cm, then back to equilibrium again. You do that full cycle once every second. You find that in your 2 m long rope, you can see one full wave. What is A) the amplitude of the wave? B) the frequency of the wave? C) the speed of the wave?

5. A periodic longitudinal wave made carefully on your Slinky has a distance of 0.5 m between successive compressions. If the wave travels with a speed of 8 m/s, what is the frequency of the wave? What is the period of the wave?

6. Relaxing on your mom’s water bed, you gently sway to the music blaring from your stereo. The speed of the wave is 5 m/s and your head bounces up and down at a frequency of 2 Hz. What is the wavelength of the wave?

Worksheet 3 - Reflection and Interference

1. Sketch roughly what the wave would look like after rebounding from a fixed end:

2. Sketch roughly what the wave would look like after it returns from the free end (tied to a light string):

3. In each of the following situations, two pulses are shown traveling toward each other. Makethree sketches showing what will happen just prior to, during and immediately after

intersection.

A) A)

B) B)

C) C)

Worksheet 4 - Standing Waves

1. Sally Sue, an enthusiastic physics student, enjoyed the opportunity to collect data from standing waves in a spring. She and her partner held the ends of their spring 4.00 m apart. There were 5 nodes in the standing wave produced. Sally moved her hand from rest position back and forth along the floor 20 times in 4.00 s. Sketch the wave, and determine the following:

A) the wavelength of the wave Sally Sue sent.

B) the frequency of the wave produced.

C) the speed of the wave.

2. What frequency and period would be required for Sally and her cheerful, pleasant, hard-working partner to produce a standing wave with three nodes? Explain.

3. If standing waves are produced in a spring and then the velocity is increased, will we see more or fewer antinodes after the increase? Why? (Assume constant frequency)

4. If standing waves are produced in a spring and then the frequency is increased, will we see more or fewer antinodes after the increase? Why? (Assume constant velocity)

5. A 60 Hz AC transformer and a magnet are used to set up a standing wave in a wire. The wire is 6.0 m long and 12 antinodes are produced in the standing wave.A) What is the wavelength of the wave?

B) What is the velocity of the wave?

C) If the velocity of the waves could be increased to 4 times its value in B), how many antinodes would there be?

Worksheet 5 - Sound

Definitions.1. Echoes demonstrate _______ of sound waves.A) refraction B) interference C) diffraction D) reflection

2. Sound is a(n) _______ wave.A) transverse B) longitudinal C) electromagnetic D) electron

3. As an approaching ambulance passes a stationary observer, the frequency of the sound emitted but its sirenA) increases. B) decreases. C) stays the same.

4. The frequency of the sound heard by the observer in question 3 _______as the approaching ambulance passes the observerA) increases. B) decreases. C) stays the same.

5. A detected change in the frequency of a sound due to a moving source or a moving observer is A) refraction B) sonar C) the Doppler Effect D) resonance

6. Which of the following does not describe the pitch of a sound?A) frequency B) a note on a scale C) loud or soft D) high or low

7. Two notes have frequencies the ratio of which is 2:1. The notes differ by a(n)A) third B) octave C) fifth D) fourth

Problems. Take the speed of sound to be 343 m/s.8. Middle C on a finely tuned piano vibrates 262 times per second. What is the period of the wave?

9. Sound travels at 5600 m/s through a steel rod. If the frequency of the waves is 2480 Hz, what is the wavelength?

10. The wavelength of a sound produced by a tuning fork is 1.3 m. The fork has a frequency of 256 Hz. What is the wave velocity?

11. A sound wave traveling at a speed of 340 m/s has a wavelength of 1.25 m. What is the frequency of the sound?

12. The human ear can detect sounds with frequencies between 20 Hz and 20 kHz. Find the largest and the smallest wavelengths of sound traveling through air at room temperature the ear can detect.

Worksheet 6- Sound

1. What would be the wavelength of a sound wave with a frequency of 500 Hz if it were traveling through water at 1435 m/s?

2. An A on the piano has a frequency of 55 Hz. What is the frequency of the A three octaves higher?

3. A bat screeches in the darkness searching for his prey. If he hears his screech echo back to him after 0.5 seconds, how far away is his dinner?

4. The echo of a ship’s foghorn, reflected from an iceberg, is heard 5.0 s after the horn is sounded. How far away is the iceberg?

5. A sound wave has a frequency of 2000 Hz and travels along a steel rod. If the distance between successive compressions is 0.40 m, what is the speed of the wave?

6. A rifle is shot in a valley formed between two parallel mountains. The echo from one mountain is heard after 2.00 s and from the other mountain 2.00 s after that. What is the width of the valley?

7. Ultrasound with a frequency of 4.25 MHz can be used to produce images of the human body. If the speed of sound in the body is the same as in salt water, 1500 m/s, what is the wavelength in the body?

9. A 448 Hz tuning fork and a 444 Hz tuning fork are struck at the same time. What is the frequency of the beat produced?

10. Two tuning forks are struck simultaneously to produce 2 beats/s. The frequency of one fork is 364 Hz. What are the possible frequencies of the other fork?

Unit 7 ReviewWaves and Sound

EquationsPeriod T=1/ f f =frequencyUniversal Wave equation v = f λ v=velocity, λ =wavelength

VocabularyAmplitudeAntinodeBeatsConstructive InterferenceCompressionCrestDestructive

InterferenceDoppler EffectExpansionFrequency HertzLongitudinal Wave Mechanical WaveMedium

NodePeriodPulse WaveResonanceShock WaveSonic BoomSpeedStanding Wave

Transverse WaveTroughWavelength

Concepts Covered Simple Harmonic Motion: Pendulums and Springs Relationships for the Period and frequency in SHM Wave Properties: Speed, frequency, wavelength, period Relationships between the wave properties Use the wave equation to solve problems - remember, its universal in that it

works for all waves - including Sound Types of waves: Transverse, Longitudinal, Mechanical, Standing Reflection of waves, and in Sound: Echoes Interference: Principle of Superposition Standing Waves: How they’re produced, location of nodes and antinodes, at

what frequencies they occur, find wavelengths, speed and frequency Sound Properties: Pitch, Loudness, etc Intensity of Sound (loudness): the Decibel Scale Doppler Effect Interference of Sound Waves Resonance in SHM, waves, and Sound Timbre of musical instruments

Review Questions1. What is the difference between the period and frequency of oscillation? How are they related?

2. Distinguish among these different parts of a wave: amplitude, crest, trough, and wavelength.

3. What does the speed of a wave depend on?

4. If the frequency of a sound is increased, what happens to the wavelength? What

happens to the speed of the wave?

5. Distinguish between a transverse and longitudinal wave. Which type of wave is sound?

6. If you triple the frequency of a vibrating object, what will happen to its period?

7. What causes a sonic boom? How fast must an airplane travel to produce one?

8. What is the pitch of a sound wave related to? What is the loudness related to?

9. Why is sound louder when a vibrating object is held to a sounding board?

10. How is resonance produced in a vibrating object?

11. What causes beats?

12. What makes instruments that play the same note sound different?

Example Problems13. A nurse counts 76 heartbeats in one minute. What are the period and frequency of the heart’s oscillations?

14. If a wave vibrates back and forth three time each second, and its crests are separated by 2 m, what is its frequency? Its period? Its speed?

15. Suppose you wanted to produce a sound wave in air that has a wavelength of 1 m. What would be the frequency?

16. A dolphin wants to know how far away the ocean floor is and sends out a squeal. If the sound echoes back to the dolphin after 0.8 seconds, how far is it to the bottom? (Hint: Sea water!)

17. A standing wave is set up in a 4-m long string that has 4 antinodes when the string is vibrated 10 times in 2 s. A) Draw the wave and label the nodes and antinodes. B) How many full waves are present? C) What is the wavelength? D) What is the frequency? E) What is the speed of the wave?

18. Two tuning forks are sounded at the same time. One has a frequency of 240 Hz, and the other is 243 Hz. What is the frequency of the beats produced?

Answers to Problems:13. T=.79 s, f=1.27 Hz

14. f =3 Hz, T= 1/3 s, v= 6 m/s15. 343 Hz16. 624 m/s17. B) 2 waves, C) λ= 2 m, D) f =5 Hz, E) v=10 m/s18. 3 Hz