1. 1) yes 2) no 3) it depends on the medium the wave is in Does a longitudinal wave, such as a sound wave, have an amplitude ? low high normalairpressurex A

2. 1) yes 2) no 3) it depends on the medium the wave is in All wave types — transverse, longitudinal, surface — have all of these properties: wavelength, frequency, amplitude, velocity, period ConcepTest 14.1Sound It Out ConcepTest 14.1 Sound It Out Does a longitudinal wave, such as a sound wave, have an amplitude ? low high normalairpressurex A

3. At a football game, the “wave” might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as? 1) polarized wave 2) longitudinal wave 3) lateral wave 4) transverse wave 5) soliton wave

4. At a football game, the “wave” might circulate through the stands and move around the stadium. In this wave motion, people stand up and sit down as the wave passes. What type of wave would this be characterized as? 1) polarized wave 2) longitudinal wave 3) lateral wave 4) transverse wave 5) soliton wave The people are moving up and down, and the wave is traveling around the stadium. Thus, the motion of the wave is perpendicular to the oscillation direction of the people, and so this is a transverse wave. ConcepTest 14.2The Wave ConcepTest 14.2 The Wave Follow-up: What type of wave occurs when you toss a pebble in a pond?

5. Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled A ? 1) 2) 3) 4) 5) zero A

6. ConcepTest 14.3aWave Motion I ConcepTest 14.3a Wave Motion I Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled A ? 1) 2) 3) 4) 5) zero The velocity of an oscillating particle momentarilyzero is (momentarily) zero at its maximum displacement. A Follow-up: What is the acceleration of the particle at point A?

7. Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled B ? 1) 2) 3) 4) 5) zero B ConcepTest 14.3bWave Motion II ConcepTest 14.3b Wave Motion II

8. Consider a wave on a string moving to the right, as shown below. What is the direction of the velocity of a particle at the point labeled B ? 1) 2) 3) 4) 5) zero The wave is moving right to the right, so the particle at B has to moving upward start moving upward in the next instant of time. B ConcepTest 14.3bWave Motion II ConcepTest 14.3b Wave Motion II Follow-up: What is the acceleration of the particle at point B?

9. t t +  t 1) 1 second 2) 2 seconds 3) 4 seconds 4) 8 seconds 5) 16 seconds A boat is moored in a fixed location, and waves make it move up and down. If the spacing between wave crests is 20 m and the speed of the waves is 5 m/s, how long does it take the boat to go from the top of a crest to the bottom of a trough ?

10. ConcepTest 14.4Out to Sea ConcepTest 14.4 Out to Sea t t +  t 1) 1 second 2) 2 seconds 3) 4 seconds 4) 8 seconds 5) 16 seconds A boat is moored in a fixed location, and waves make it move up and down. If the spacing between wave crests is 20 m and the speed of the waves is 5 m/s, how long does it take the boat to go from the top of a crest to the bottom of a trough ? v = f = / T, T = / v = 20 m v = 5 m/sT = 4 secs We know that: v = f = / T, hence T = / v. If = 20 m and v = 5 m/s, so T = 4 secs. T/2half a period 2 secs The time to go from a crest to a trough is only T/2 (half a period), so it takes 2 secs !!

11. 1) 0.3 mm 2) 3 cm 3) 30 cm 4) 300 m 5) 3 km Microwaves travel with the speed of light, c = 3  10 8 m/s. At a frequency of 10 GHz these waves cause the water molecules in your burrito to vibrate. What is their wavelength? 1 GHz = 1 Gigahertz = 10 9 cycles/sec H H O

12. ConcepTest 14.5Lunch Time ConcepTest 14.5 Lunch Time We know v wave = / T = f so = v / f = = 3  10 -2 m = 3 cm = 3  10 -2 m = 3 cm 3  10 8 m /s 10  10 9 Hz 1) 0.3 mm 2) 3 cm 3) 30 cm 4) 300 m 5) 3 km Microwaves travel with the speed of light, c = 3  10 8 m/s. At a frequency of 10 GHz these waves cause the water molecules in your burrito to vibrate. What is their wavelength? 1 GHz = 1 Gigahertz = 10 9 cycles/sec H H O

13. A wave pulse can be sent down a rope by jerking sharply on the free end. If the tension of the rope is increased, how will that affect the speed of the wave? 1) speed increases 2) speed does not change 3) speed decreases

14. A wave pulse can be sent down a rope by jerking sharply on the free end. If the tension of the rope is increased, how will that affect the speed of the wave? 1) speed increases 2) speed does not change 3) speed decreases The wave speed depends on the square root of the tension, so if the tension increases, then the wave speed will also increase. ConcepTest 14.6aWave Speed I ConcepTest 14.6a Wave Speed I

15. A wave pulse is sent down a rope of a certain thickness and a certain tension. A second rope made of the same material is twice as thick, but is held at the same tension. How will the wave speed in the second rope compare to that of the first? 1) speed increases 2) speed does not change 3) speed decreases

16. A wave pulse is sent down a rope of a certain thickness and a certain tension. A second rope made of the same material is twice as thick, but is held at the same tension. How will the wave speed in the second rope compare to that of the first? 1) speed increases 2) speed does not change 3) speed decreases The wave speed goes inversely as the square root of the mass per unit length, which is a measure of the inertia of the rope. So in a thicker (more massive) rope at the same tension, the wave speed will decrease. ConcepTest 14.6bWave Speed II ConcepTest 14.6b Wave Speed II

17. A length of rope L and mass M hangs from a ceiling. If the bottom of the rope is jerked sharply, a wave pulse will travel up the rope. As the wave travels upward, what happens to its speed? Keep in mind that the rope is not massless. 1) speed increases 2) speed does not change 3) speed decreases

18. A length of rope L and mass M hangs from a ceiling. If the bottom of the rope is jerked sharply, a wave pulse will travel up the rope. As the wave travels upward, what happens to its speed? Keep in mind that the rope is not massless. 1) speed increases 2) speed does not change 3) speed decreases The tension in the rope is not constant in the case of a massive rope! The tension increases as you move up higher along the rope, because that part of the rope has to support all of the mass below it! Since the tension increases as you go up, so does the wave speed. ConcepTest 14.6cWave Speed III ConcepTest 14.6c Wave Speed III

19. 1) the frequency f 2) the wavelength 3) the speed of the wave 4) both f and 5) both v wave and When a sound wave passes from air into water, what properties of the wave will change?

20. ConcepTest 14.7a ConcepTest 14.7a Sound Bite I 1) the frequency f 2) the wavelength 3) the speed of the wave 4) both f and 5) both v wave and When a sound wave passes from air into water, what properties of the wave will change? Wave speed must change (different medium). Frequency does not change (determined by the source). v = f vf Now, v = f and since v has changed and f is constant must also change then must also change. Follow-up: Does the wave speed increase or decrease in water?

21. If you fill your lungs with helium and then try talking, you sound like Donald Duck. What conclusion can you reach about the speed of sound in helium? 1) speed of sound is less in helium 2) speed of sound is the same in helium 3) speed of sound is greater in helium 4) this effect has nothing to do with the speed in helium

22. If you fill your lungs with helium and then try talking, you sound like Donald Duck. What conclusion can you reach about the speed of sound in helium? 1) speed of sound is less in helium 2) speed of sound is the same in helium 3) speed of sound is greater in helium 4) this effect has nothing to do with the speed in helium The higher pitch implies a higher frequency. In turn, since v = f, this means that the speed of the wave has increased (as long as the wavelength, determined by the length of the vocal chords, remains constant). ConcepTest 14.8c ConcepTest 14.8c Speed of Sound III Follow-up: Why is the speed of sound greater in helium than in air?

23. You stand a certain distance away from a speaker and you hear a certain intensity of sound. If you double your distance from the speaker, what happens to the sound intensity at your new position? 1) drops to 1/2 its original value 2) drops to 1/4 its original value 3) drops to 1/8 its original value 4) drops to 1/16 its original value 5) does not change at all ConcepTest 14.10a ConcepTest 14.10a Sound Intensity I

24. You stand a certain distance away from a speaker and you hear a certain intensity of sound. If you double your distance from the speaker, what happens to the sound intensity at your new position? 1) drops to 1/2 its original value 2) drops to 1/4 its original value 3) drops to 1/8 its original value 4) drops to 1/16 its original value 5) does not change at all distance doubles decrease to one-quarter For a source of a given power P, the intensity is given by I = P/4  r 2. So if the distance doubles, the intensity must decrease to one-quarter its original value. ConcepTest 14.10a ConcepTest 14.10a Sound Intensity I Follow-up: What distance would reduce the intensity by a factor of 100?

25. (1) the long pipe (2) the short pipe (3) both have the same frequency (4) depends on the speed of sound in the pipe You have a long pipe and a short pipe. Which one has the higher frequency?

26. shorter pipe shorter wavelength frequency has to be higher A shorter pipe means that the standing wave in the pipe would have a shorter wavelength. Since the wave speed remains the same, the frequency has to be higher in the short pipe. (1) the long pipe (2) the short pipe (3) both have the same frequency (4) depends on the speed of sound in the pipe You have a long pipe and a short pipe. Which one has the higher frequency? ConcepTest 14.12a ConcepTest 14.12a Pied Piper I

27. A wood whistle has a variable length. You just heard the tone from the whistle at maximum length. If the air column is made shorter by moving the end stop, what happens to the frequency? 1) frequency will increase 2) frequency will not change 3) frequency will decrease

28. A wood whistle has a variable length. You just heard the tone from the whistle at maximum length. If the air column is made shorter by moving the end stop, what happens to the frequency? 1) frequency will increase 2) frequency will not change 3) frequency will decrease shorter pipe shorter wavelength v = f frequency has to increase A shorter pipe means that the standing wave in the pipe would have a shorter wavelength. Since the wave speed remains the same, and since we know that v = f, then we see that the frequency has to increase when the pipe is made shorter. ConcepTest 14.12b ConcepTest 14.12b Pied Piper II

29. If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change? 1) frequency will increase 2) frequency will not change 3) frequency will decrease

30. If you blow across the opening of a partially filled soda bottle, you hear a tone. If you take a big sip of soda and then blow across the opening again, how will the frequency of the tone change? 1) frequency will increase 2) frequency will not change 3) frequency will decrease longer pipe longer wavelength v = f frequency has to be lower By drinking some of the soda, you have effectively increased the length of the air column in the bottle. A longer pipe means that the standing wave in the bottle would have a longer wavelength. Since the wave speed remains the same, and since we know that v = f, then we see that the frequency has to be lower. ConcepTest 14.12c ConcepTest 14.12c Pied Piper III Follow-up: Why doesn’t the wave speed change?

31. 1) depends on the speed of sound in the pipe 2) you hear the same frequency 3) you hear a higher frequency 4) you hear a lower frequency You blow into an open pipe and produce a tone. What happens to the frequency of the tone if you close the end of the pipe and blow into it again?

32. open pipe1/2 of a wave closed pipe 1/4 of a wave wavelength is larger in the closed pipefrequency will be lower In the open pipe, 1/2 of a wave “fits” into the pipe, while in the closed pipe, only 1/4 of a wave fits. Because the wavelength is larger in the closed pipe, the frequency will be lower. 1) depends on the speed of sound in the pipe 2) you hear the same frequency 3) you hear a higher frequency 4) you hear a lower frequency You blow into an open pipe and produce a tone. What happens to the frequency of the tone if you close the end of the pipe and blow into it again? ConcepTest 14.13 ConcepTest 14.13 Open and Closed Pipes Follow-up: What would you have to do to the pipe to increase the frequency?

33. When you tune a guitar string, what physical characteristic of the string are you actually changing? 1) the tension in the string 2) the mass per unit length of the string 3) the composition of the string 4) the overall length of the string 5) the inertia of the string

34. When you tune a guitar string, what physical characteristic of the string are you actually changing? 1) the tension in the string 2) the mass per unit length of the string 3) the composition of the string 4) the overall length of the string 5) the inertia of the string changing the tension By tightening (or loosening) the knobs on the neck of the guitar, you are changing the tension in the string. This alters the wave speed and therefore alters the frequency of the fundamental standing wave because f = v/2L. Follow-up: To increase frequency, do you tighten or loosen the strings?

35. Observers A, B and C listen to a moving source of sound. The location of the wave fronts of the moving source with respect to the observers is shown below. Which of the following is true? 1) frequency is highest at A 2) frequency is highest at B 3) frequency is highest at C 4) frequency is the same at all three points ConcepTest 14.15a ConcepTest 14.15a Doppler Effect I

36. Observers A, B and C listen to a moving source of sound. The location of the wave fronts of the moving source with respect to the observers is shown below. Which of the following is true? 1) frequency is highest at A 2) frequency is highest at B 3) frequency is highest at C 4) frequency is the same at all three points observer C The number of wave fronts hitting observer C per unit time is greatest – thus the observed frequency is highest there. ConcepTest 14.15a ConcepTest 14.15a Doppler Effect I Follow-up: Where is the frequency lowest?

37. You are heading toward an island in a speedboat and you see your friend standing on the shore, at the base of a cliff. You sound the boat’s horn to alert your friend of your arrival. If the horn has a rest frequency of f 0, what frequency does your friend hear ? 1) lower than f 0 2) equal to f 0 3) higher than f 0

38. You are heading toward an island in a speedboat and you see your friend standing on the shore, at the base of a cliff. You sound the boat’s horn to alert your friend of your arrival. If the horn has a rest frequency of f 0, what frequency does your friend hear ? 1) lower than f 0 2) equal to f 0 3) higher than f 0 approach of the source frequency is shifted higher Due to the approach of the source toward the stationary observer, the frequency is shifted higher. This is the same situation as depicted in the previous question. ConcepTest 14.15b ConcepTest 14.15b Doppler Effect II

39. A string is clamped at both ends and plucked so it vibrates in a standing mode between two extreme positions a and b. Let upward motion correspond to positive velocities. When the string is in position b, the instantaneous velocity of points on the string: a b 1) is zero everywhere 2) is positive everywhere 3) is negative everywhere 4) depends on the position along the string

40. Observe two points: Just before b Just after b Both points change direction before and after b, so at b all points must have zero velocity. ConcepTest 14.17aStanding Waves I ConcepTest 14.17a Standing Waves I A string is clamped at both ends and plucked so it vibrates in a standing mode between two extreme positions a and b. Let upward motion correspond to positive velocities. When the string is in position b, the instantaneous velocity of points on the string: 1) is zero everywhere 2) is positive everywhere 3) is negative everywhere 4) depends on the position along the string

41. a b c A string is clamped at both ends and plucked so it vibrates in a standing mode between two extreme positions a and b. Let upward motion correspond to positive velocities. When the string is in position c, the instantaneous velocity of points on the string: 1) is zero everywhere 2) is positive everywhere 3) is negative everywhere 4) depends on the position along the string

42. direction depends on the location When the string is flat, all points are moving through the equilibrium position and are therefore at their maximum velocity. However, the direction depends on the location of the point. Some points are moving upward rapidly, and some points are moving downward rapidly. a b c ConcepTest 14.17bStanding Waves II ConcepTest 14.17b Standing Waves II A string is clamped at both ends and plucked so it vibrates in a standing mode between two extreme positions a and b. Let upward motion correspond to positive velocities. When the string is in position c, the instantaneous velocity of points on the string: 1) is zero everywhere 2) is positive everywhere 3) is negative everywhere 4) depends on the position along the string

43. Pair 1Pair 2 1) pair 1 2) pair 2 3) same for both pairs 4) impossible to tell by just looking The traces below show beats that occur when two different pairs of waves interfere. For which case is the difference in frequency of the original waves greater?

44. Pair 1Pair 2 difference in frequency f beat = f 2 – f 1 Recall that the beat frequency is the difference in frequency between the two waves: f beat = f 2 – f 1 greater beat frequency greater frequency difference Pair 1 has the greater beat frequency (more oscillations in same time period), so Pair 1 has the greater frequency difference. 1) pair 1 2) pair 2 3) same for both pairs 4) impossible to tell by just looking The traces below show beats that occur when two different pairs of waves interfere. For which case is the difference in frequency of the original waves greater? ConcepTest 14.18 ConcepTest 14.18 Beats