A1 Conceptual Physics
Spring 2011
Waves and Sound
Chapters 25 & 26
Conceptual Physics Waves & Sound Outline
Hewitt: Chapter 25 & 26
Exercises: 12 Waves and Sound
Fill in the Charts completely
Variables introduced or used in chapter:
Quantity
Symbol
Units
Frequency
Wavelength
Wave Speed
Length of string
number of antinodes
Length of pipe
Formula Chart*
Wave Speed
Relationship between Frequency and
Period
Wave in String Frequency
Wave in Pipe Frequency
Beat Frequency
Define the following terms using COMPLETE SENTENCES:
Vibration
Period
Simple Harmonic Motion
Sine Curve
Crest
Trough
Amplitude
Wavelength
Frequency
Transverse Wave
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Spring 2011
Longitudinal Wave
Waves and Sound
Chapters 25 & 26
Constructive Interference
Destructive Interference
In Phase
Out of Phase
Standing Wave
Hertz
Doppler Effect
Node
Antinodes
Fundamental Frequency
Overtones
Beats
Bow Waves
Shock Waves
Sonic Boom
Compression
Pitch
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Spring 2011
Infrasonic
Waves and Sound
Chapters 25 & 26
Ultrasonic
Rarefaction
Loudness
Forced Vibrations
Natural Frequency
Resonance
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Spring 2011
Waves and Sound
Chapters 25 & 26
Waves & Sound Homework Help
Intensity (W/m2)
1 x 10-12
1 x 10-11
1 x 10-10
1 x 10-9
1 x 10-8
1 x 10-7
1 x 10-6
1 x 10-5
1 x 10-4
1 x 10-3
1 x 10-2
1 x 10-1
1 x 100
1 x 101
1 x 103
Conversion of Intensity to decibel level
Decibel level (dB)
Examples
0
Threshold of hearing
10
Rustling leaves
20
Quiet whisper
30
Whisper
40
Mosquito buzzing
50
Normal conversation
60
Air conditioning at 6 m
70
Vacuum cleaner
80
Busy traffic, alarm clock
90
Lawn mower
100
Subway, power motor
110
Auto horn at 1 m
120
Threshold of pain
130
Thunderclap, machine gun
150
Nearby jet airplane
Formulas: T = 1/ f f = 1/ T
(T = Period and f = Frequency)
Wave Velocity = (Frequency)(Wavelength)
v=λf
v=d/t
Speed of Sound in Air V = 330 + 0.6 (degrees Celsius)
Beats =Frequency of LARGER tuning fork - Frequency of SMALLER tuning fork
(Beats are never negative)
Distance when an echo is involved = speed of sound / half the time
Fundamental Frequency
Harmonic Frequency
Values of n
String Waves
n = 1, 2, 3 , …
Open Tube
n = 1, 2, 3 , …
Closed Tube
n = 1, 3 , 5, …
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A1 Conceptual Physics
Spring 2011
Waves and Sound
Chapters 25 & 26
Waves and Sound Homework
Wave Speed
1. A piano plays the note A at a frequency of 440 hertz. What is the approximate
wavelength of this sound wave if the speed of sound in air is 340 m/s? [0.77 m]
2. An ocean wave has a frequency of 2 Hz and a speed of 20 m/sec. What is the
wavelength of this wave? [10 m]
3. A tuning fork has a frequency of 280 hertz and the wavelength of the sound
produced is 1.5 meters. Calculate the velocity of the wave. [420 m/s]
4. A wave moving along a rope has a wavelength of 1.2 meters and a frequency of
4.5 hertz. How fast is the wave traveling along the rope? [5.4 m/s]
5: A jump rope is shaken producing a wave with a wavelength of 0.5m with the
crest of the wave passing a certain point 4 times per second (4 Hz). What is the
velocity of the wave? [2 m/s]
6: A wave has a period of 6 seconds. What is the frequency? [0.17 Hz]
7: It takes 3 seconds for one complete wave. What is its period? What is its
frequency? [3 s, 1/3 Hz]
8: If the amplitude of a wave is doubled, how much more energy does the wave now
have? [4 x’s]
9: Redraw and Label the wave below with amplitude, crest, trough, wavelength &
equilibrium line. What type of wave is this?
10. Sketch and label a diagram showing 6.0 s of a transverse wave that has a period
of 3.0 s, a wavelength of 15 cm, and an amplitude of 10 cm. What is the speed of
this wave? [0.05 m/s]
11. Lupert skipped school one day and went to Lake Conroe. While he was sitting
on a dock reading his physics book, a motorboat came by. Lupert noticed that three
crests from the waves reached the dock every five seconds, and that the distance
between crests was two meters. Use this information to calculate the velocity,
period, frequency, and wavelength of these waves. [1.2 m/s, 1.67 s, 0.6 Hz, 2 m]
12: How long should a string be in order to produce a standing wave with nine
antinodes using a string vibrator of 180 Hz if the tension is adjusted so that the
speed of the wave is 34 m/s? [0.85 m]
13: Lupert skipped school again. This time he saw a boat make waves in the water
such that five crests reached the dock every six seconds. The distance between
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A1 Conceptual Physics
Waves and Sound
Spring 2011
Chapters 25 & 26
adjacent crests was three meters. Calculate the frequency, period, wavelength, and
speed of these waves. [0.83 Hz, 1.2 s, 3 m, 2.5 m/s]
Interference
14: Draw an example of constructive interference.
15: Draw an example of destructive interference.
16. What is the difference between complete destructive interference & partial
destructive interference?
17: Draw an example of a wave pulse that travels down a string and is reflected
from a free end.
18. Draw the situation if it is reflected from a fixed end.
Speed of sound
19. Sound pulses emitted by a dolphin travel through 20oC ocean water at a rate of
1450 m/s. In 20oC air, these pulses would travel 343 m/s. How can you account for
the difference in speed?
20: Give the speed of sound through air at each temperature:
a. 14.6 C [339.76 m/s]
b. 25.7 C [346.42 m/s]
21 Give the air temperature when the speed of sound is:
a. 356.8 m/s [43o C]
b. 326.4 m/s [-7.67o C]
22: What is the frequency of sound in air at 25 C having a wavelength of 0.84 m?
[411.9 Hz]
Canyon / Echo Problems
23: Polly is standing on the bottom of a wide canyon, leaning against its wall. She
shouts “hello” toward the opposite side of the canyon. If the speed of sound is
340m/sec and Polly hears her own echo 4 seconds later, how wide is the canyon?
[680 m]
24: The speed of sound in air is 330 m/s and a girl hears her echo in 9 secs. How far
away is the wall where the sound echoed? [1485m]
Intensity
25: When the decibel level of traffic in the street goes from 40 to 60 db, how much
louder does the traffic noise seem? How much greater is the intensity?
26: When a guitar string is “plucked” it vibrates at its fundamental. If a guitar string
is 0.68m long, what is the speed of the wave on the string if the fundamental
frequency of the guitar string is 262 hertz? [356.32 m/s]
Open Tube
27. Calculate the speed of sound if a 292 Hz tuning fork resonates in an open tube
when it is 28.7 cm long. [167.61 m/s]
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Waves and Sound
Spring 2011
Chapters 25 & 26
28: What are the first three harmonic frequencies in a 0.68 m long pipe that is open
at both ends? Use the speed of sound in air is 345 m/s. Label your answers with the
appropriate harmonic number. [n=1, 253.68 Hz; n=2, 507.35 Hz; n=3, 761.03 Hz]
29: What are the first three harmonic frequencies in a 0.75 m long pipe that is open
at both ends? Assume that the speed of sound in air is 338 m/s. Label your answers
with the appropriate harmonic number. [n=1, 112.67Hz; n=3, 338Hz; n=5, 563.3Hz]
Closed Tube
30. Calculate the speed of sound if a 464 Hz tuning fork resonates in a closed tube
that is 18.0 cm long. [334.08 m/s]
31. Calculate the speed of sound if a 292 Hz tuning fork resonates in a closed tube
when it is 28.7 cm long. [335.126 m/s]
32: What are the first three harmonic frequencies in a 0.68 m long pipe that is
closed at one end? Assume that the speed of sound in air is 345 m/s. Label your
answers with the appropriate harmonic number. [n=1, 126.84 Hz; n=3, 380.51 Hz;
n=5, 634.19 Hz]
33. What are the first three harmonic frequencies in a 0.75 m long pipe that is
closed at one end? Assume that the speed of sound in air is 338 m/s. Label your
answers with the appropriate harmonic number. [n=1, 112.67 Hz; n=3, 338 Hz;
n=5, 563.3 Hz]
Beats
34: An orchestra tunes their instruments. They hear a throbbing sound. If one
instrument's note is 500 Hz and another instrument playing 512 Hz are playing at
the same time, what is the beat frequency? [12 beats per second (12 Hz)]
35: A tuning fork with a frequency of 600 hertz causes beats when played at the
same time as another tuning fork. If the beat frequency is 30 beats per second, what
is the frequency of the second tuning fork? [570 Hz or 630 Hz]
Doppler
36. If you hear a higher pitch from a trumpet than from a saxophone, how do the
frequencies of the sound waves from the trumpet compare to the frequencies of the
saxophone?
37: Dolphins can produce sound waves with frequencies ranging from 0.25 kHz –
220 kHz, but only those at the upper end of the spectrum are used in echolocation.
Explain why the high frequency waves work better than low frequency waves.
38: If a police car is coming towards you, will its pitch sound higher or lower than if
it was at rest next to you?
39. Opera singers have been known to set crystal goblets in vibration with their
powerful voices. In fact, an amplified human voice can shatter the glass, but only at
certain fundamental frequencies. Speculate about why only certain frequencies will
break the glass.
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A1 Conceptual Physics
Spring 2011
Waves and Sound
Chapters 25 & 26
Waves and Sound Energy Station Lab #1
PROBLEM:
MATERIALS &
PROCEDURE:
What observations can be made on the properties and
behaviors of waves and sound based on the lab stations?
Listed for each station.
STATION 1: MATERIALS:
ring stand, ping pong ball, string, tuning fork,
beaker filled with water, rubber hammer
PROCEDURES and OBSERVATIONS:
1. Gently tap the tuning fork with the hammer and bring the
tuning fork close to your ear. What do you observe?
2. Look at the prongs of the tuning fork while it is making a
sound. What do you observe?
3. Gently tap the tuning fork with the hammer and let the tuning
fork barely touch the ping pong ball hanging. What happens and
why?
4. Gently tap the tuning fork again with the hammer and touch
the tuning fork to the surface of the water in the beaker. What
happens and why?
5. As sound travels, explain what happens to the molecules.
STATION 2: MATERIALS:
Three resonance boxes, rubber hammer (2 boxes
rd
with same frequency & 3 box with different frequency)
PROCEDURES and OBSERVATIONS:
1. Gently strike resonance box A's tuning fork with the opening
facing resonance box B's open end. Stop box A's tuning fork
from vibrating. Do you hear a sound? Explain what happened
and why.
2. Gently strike resonance box A's tuning fork with the opening
facing resonance box C's open end. Stop box A's tuning fork
from vibrating. Do you hear a sound? Explain what happened
and why.
3. Gently strike resonance box A's tuning fork and then strike
resonance box C's tuning fork so that they "play" at the same
time. What do you hear? Explain what happened and why.
4. Gently strike resonance box A's tuning fork and then strike
resonance box B's tuning fork so that they "play" at the same
time. What do you hear? Explain what happened and why.
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A1 Conceptual Physics
Spring 2011
STATION 3: MATERIALS:
band
Waves and Sound
Chapters 25 & 26
three bottles filled with different levels of water, rubber
PROCEDURES and OBSERVATIONS:
1. Blow across the top of each bottle. Which bottle had the
highest pitch? Why?
2. Which bottle had the lowest pitch? Why?
3. Hold the rubber band at different tensions and pluck it.
Explain how the pitch changes.
4. Describe how thickness, tightness and length affect the pitch
of a musical instrument.
STATION 4: MATERIALS:
slinky
SAFETY ALERT: DO NOT let go of the slinky or it will may be destroyed. Any damage
to slinky will result in -20 for each team member.
PROCEDURES and OBSERVATIONS:
1. Stretch out the slinky and push some of the springs together
and let it go while having team members hold both ends of the
slinky. Describe what happens to the compression.
2. Is this a transverse or longitudinal wave? How do you know?
3. Draw the wave below and label a compression and
rarefaction.
CONCLUSION: Explain at least 3 things you understand better about waves & sound
having completed this lab.
Rubric: Each question: 5 pts x 16 = 80 pts
Conclusion: 20 Pts
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A1 Conceptual Physics
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Waves and Sound
Chapters 25 & 26
Standing Waves Lab #2
Theory: Each harmonic is the number of antinodes in the string. One complete
wavelength is the length of two antinodes. If the string is 1 meter long and you
have 3 antinodes then the wavelength is 2/3 meter, since 3 antinodes equal 1
meter and a whole wave is 2 of the 3 antinodes. The larger the amplitude of a
wave, the more energy the wave has, because it takes more force to stretch the
string a greater distance. The wiggler applies electrical energy to vibrate the
string. The wiggler supplies about the same amount of energy to each harmonic.
Purpose: To observe how frequency relates to standing waves.
Materials: CPO Wave Generator CPO Wiggler CPO Timer
Ruler
Procedure:
1. Turn on timer and set the wave generator to WAVES.
2. Set the timer to measure FREQUENCY. You should get a reading of about 10 Hz,
which means the wiggler is oscillating back and forth 10 times per second.
3. Adjust the frequency of the wiggler with the frequency control on the Wave
Generator.
4. Adjust the frequency to obtain the 2nd harmonic of the string
5. Fine-tune the frequency to obtain the largest amplitude before recording the
data.
6. Record the frequency, wavelength and amplitude in the data tables below. Use a
ruler to measure the amplitude of the wave patterns for 6 different harmonics,
including the 6th harmonic or one higher. Remember the amplitude is ½ the
width of the wave at the widest point.
7. Find and record the 3rd, 4th, and 5th harmonics.
8. Try to find the 1st harmonic. Use the data you collected to help find it.
9. Calculate the velocity of the waves. Show at least one sample calculation.
Write an Hypothesis for this lab: (5 pts)
Observations: Make chart on paper (25 x 2 = 50 pts )
Harmonic #
Frequency
Wavelength
(Hz)
(m)
Speed of wave
(m/s)
Analysis: (5 pts x 3 = 15 pts)
1. Describe how the frequencies of the different harmonic patterns are related
to each other. Does the pattern closely resemble what we discussed in
lecture?
2. If the frequency increases, what happens to the wavelength?
3. Make an amplitude vs. frequency graph on a separate piece of graph paper
and attach to the lab. Label axes (with units), include a title, make as large
as is reasonable, and use a curved “best fit” line. (20 pts)
Conclusion: (30 pts) Write a paragraph (min of 5 sentences) with topic sentence.
Summarize the lab and identify all of the variables. What did you learn? Describe how
frequency and wavelength are related.
Waves and Sound 52
Amplitude
(cm)
A1 Conceptual Physics
Spring 2011
Waves and Sound Review Sheet – TURN IN BEFORE TEST
Waves and Sound
Chapters 25 & 26
1. Define.
a. Wave:
b. Pulse Wave:
c. Periodic Wave:
d. Medium:
e. Mechanical Wave:
f. Electromagnetic Wave:
g. Longitudinal Wave ( P Wave) :
h. Transverse Wave ( S Wave) :
i. Crest :
j. Trough:
k. Amplitude:
l. Equilibrium (nodal) line
2. The number of wavelengths that pass a point in a certain time period is called the
______________ of the wave and is represented with the variable _____ and measured in
_____________
3. The time it takes one wavelength to occur is called the _________________ and is
represented with the variable _____ and measured in _______
4. Sketch and label all parts of a (a) transverse wave and a (b) longitudinal wave:
5. _____________________________ is the overlapping of two or more waves.
6. When two or more waves interfere to form a larger wave it is called ___________________
7. When two or more waves interfere to become a smaller wave it is called _____________
8. Name some instruments that produce sound waves
9. If a cannon goes off in space, is it quieter or louder than on Earth’s surface?
10. ________________________ is what happens when a wave reaches a boundary.
11. The reflected wave at a free boundary is (opposite, identical ) to the sent wave.
The reflected wave at a fixed boundary is (opposite, identical) to the sent wave.
12. All sound is created by a _________________ object.
13. Sound Waves are ___________ waves meaning they require a _________ through which
to travel.
14. Humans hear frequencies between _____ and ___________ Hertz.
15. Any frequency below 20 Hz is called _________________
Any frequency above 20,000 is called __________________
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Waves and Sound
Spring 2011
Chapters 25 & 26
16. Sound generally travels fastest through _________ slower through _______ and slowest
through ______
17. When sound waves interact constructively the sound gets ____ when they interact
destructively the sound gets _______________
18. Wavelength is _________________ related to frequency.
19. Generally, when the temperature of the medium increases the speed of sound in the
medium ____
20. What do we call the phenomena when the pitch of a sound from a sound producer
moving toward the observer gets higher and the pitch of the sound gets lower when the
sound producer is moving away from the observer? ______________________
21. The relative intensity of sound is measured in ______________
The level you can barely hear is called the _________________________________
and the level that causes injury is called the ____________________________
22. What part of the ear is circular and resonates at different frequencies?
23. When the intensity of sound is multiplied by 10 the decibels increase by _______
An increase of 10 dB makes the sound roughly _____________ as loud.
24. A guitar string produces a _____________ _______________ in the body of the guitar which
amplifies the sound.
25. When a object is vibrating at its own natural frequency without being touched it is
said to be ______________
26. A ______________ ___ ___________ is produced when two waves of the same frequency
and wavelength traveling in opposite directions interfere with each other in alternating
regions of ________________________ (at node) and _______________________________ (at antinode).
27. The _____________ harmonic consists of two nodes and an antinode. It is also referred
to as the ______________________ harmonic
28. The frequency of a harmonic on a string or open ended pipe is determined using the
equation:____
29. The frequency of a harmonic on a string or open ended pipe is determined using the
equation For a closed pipe it is: ____________________
30. A ___________ is an area of destructive interference on a standing wave and an
______________ is an area of constructive interference.
31. _______________ are heard when sounds of different frequencies are interacting
constructively and destructively in succession. The number of beats you hear every
second is the difference between the two _______________________.
Waves and Sound 54
A1 Conceptual Physics
Waves and Sound
Spring 2011
Chapters 25 & 26
32. Earthquakes can produce three types of waves. One of these is a transverse wave
called an S wave. A typical S wave travels at 5000 m/s. Its wavelength is about 417
meters. What is its frequency? [ 11.99 Hz]
33. A wave has a frequency of 50 hertz and a wavelength of 6 meters. What is the
wave's velocity?[300 m/s]
34. A wave is moving toward shore with a velocity of 5 m/sec. if its frequency is 2.5
hertz what is its wavelength? [2 m]
35. A hiker shouts toward a vertical cliff 826 m away. The echo is heard 4.84 s later.
a. What is the speed of this sound wave in the air? [341.32 m/s]
b. What is the wavelength and period of this wave if its frequency is 456 Hz?
[0.75 m, 0.002 sec]
36. If the air temperature is 20 C, what are the three shortest open-end tube lengths
that will resonate with a 400 Hz tuning fork, and what are the three shortest closed-end
tube lengths that will resonate with it?
a. open tubes [0.43 m, 0.86 m, 1.29 m]
b. closed tubes [0.21m, 0.64 m, 1.07m]
37. You dip your finger into a pan of water twice each second, producing waves with
troughs that are separated by 0.15 m. Calculate the wave’s frequency, period,
wavelength, and speed. [0.5 Hz, 2 sec, 0.15 m, 0.075 m/s]
38. How long should a string be in order to produce a standing wave with nine
antinodes using a string vibrator of 180 Hz if the tension is adjusted so that the speed
of the wave is 34 m/s?[ 0.86 m]
39. A piano tuner using a 392 Hz tuning fork to tune the wire for G-natural hears four
beats per second. What are the two possible frequencies of vibration of this piano wire?
[388 Hz & 396 Hz]
Waves and Sound 55