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2. ConcepTest 11.1a ConcepTest 11.1a Harmonic Motion I a) 0 b) A/2 c) A d) 2A e) 4A A mass on a spring in SHM has amplitude A and period T. What is the total distance traveled by the mass after a time interval T?

3. ConcepTest 11.1a ConcepTest 11.1a Harmonic Motion I a) 0 b) A/2 c) A d) 2A e) 4A A mass on a spring in SHM has amplitude A and period T. What is the total distance traveled by the mass after a time interval T? time interval T complete oscillation The distance it covers is: A + A + A + A (4A). In the time interval T (the period), the mass goes through one complete oscillation back to the starting point. The distance it covers is: A + A + A + A (4A).

4. ConcepTest 11.2 ConcepTest 11.2 Speed and Acceleration a) x = A b) x > 0 but x < A c) x = 0 d) x < 0 e) none of the above A mass on a spring in SHM has amplitude A and period T. At what point in the motion is v = 0 and a = 0 simultaneously?

5. ConcepTest 11.2 ConcepTest 11.2 Speed and Acceleration a) x = A b) x > 0 but x < A c) x = 0 d) x < 0 e) none of the above A mass on a spring in SHM has amplitude A and period T. At what point in the motion is v = 0 and a = 0 simultaneously? If both v and a would be zero at the same time, the mass would be at rest and stay at rest! NO pointv a If both v and a would be zero at the same time, the mass would be at rest and stay at rest! Thus, there is NO point at which both v and a are both zero at the same time. Follow-up: Where is acceleration a maximum?

6. A mass oscillates in simple harmonic motion with amplitude A. If the mass is doubled, but the amplitude is not changed, what will happen to the total energy of the system? a) total energy will increase b) total energy will not change c) total energy will decrease ConcepTest 11.5a ConcepTest 11.5a Energy in SHM I

7. A mass oscillates in simple harmonic motion with amplitude A. If the mass is doubled, but the amplitude is not changed, what will happen to the total energy of the system? a) total energy will increase b) total energy will not change c) total energy will decrease The total energy is equal to the initial value of the elastic potential energy, which is PE s = 1/2 kA 2. This does not depend on mass, so a change in mass will not affect the energy of the system. ConcepTest 11.5a ConcepTest 11.5a Energy in SHM I Follow-up: What happens if you double the amplitude?

8. If the amplitude of a simple harmonic oscillator is doubled, which of the following quantities will change the most? a) frequency b) period c) maximum speed d) maximum acceleration e) total mechanical energy ConcepTest 11.5b ConcepTest 11.5b Energy in SHM II

9. If the amplitude of a simple harmonic oscillator is doubled, which of the following quantities will change the most? a) frequency b) period c) maximum speed d) maximum acceleration e) total mechanical energy Frequency and period do not depend on amplitude at all, so they will not change. Maximum acceleration and maximum speed do depend on amplitude, and both of these quantities will double (you should think about why this is so). The total energy equals the initial potential energy, which depends on the square of the amplitude, so that will quadruple. ConcepTest 11.5b ConcepTest 11.5b Energy in SHM II Follow-up: Why do maximum acceleration and speed double?

10. A glider with a spring attached to each end oscillates with a certain period. If the mass of the glider is doubled, what will happen to the period? a) period will increase b) period will not change c) period will decrease ConcepTest 11.6a ConcepTest 11.6a Period of a Spring I

11. A glider with a spring attached to each end oscillates with a certain period. If the mass of the glider is doubled, what will happen to the period? a) period will increase b) period will not change c) period will decrease The period is proportional to the square root of the mass. So an increase in mass will lead to an increase in the period of motion. T = 2  ( m / k ) ConcepTest 11.6a ConcepTest 11.6a Period of a Spring I Follow-up: What happens if the amplitude is doubled?

12. Two pendula have the same length, but different masses attached to the string. How do their periods compare? a) period is greater for the greater mass b) period is the same for both cases c) period is greater for the smaller mass ConcepTest 11.8a ConcepTest 11.8a Period of a Pendulum I

13. Two pendula have the same length, but different masses attached to the string. How do their periods compare? a) period is greater for the greater mass b) period is the same for both cases c) period is greater for the smaller mass The period of a pendulum depends on the length and the acceleration due to gravity, but it does not depend on the mass of the bob. T = 2  ( L / g ) ConcepTest 11.8a ConcepTest 11.8a Period of a Pendulum I Follow-up: What happens if the amplitude is doubled?

14. a) period increases b) period does not change c) period decreases A swinging pendulum has period T on Earth. If the same pendulum were moved to the Moon, how does the new period compare to the old period? ConcepTest 11.10c ConcepTest 11.10c Pendulum in Elevator III

15. The acceleration due to gravity is smaller on the Moon. The relationship between the period and g is given by: if g gets smaller, T will increase therefore, if g gets smaller, T will increase. g L T  22 a) period increases b) period does not change c) period decreases A swinging pendulum has period T on Earth. If the same pendulum were moved to the Moon, how does the new period compare to the old period? ConcepTest 11.10c ConcepTest 11.10c Pendulum in Elevator III Follow-up: What can you do to return the pendulum to its original period?

16. After a pendulum starts swinging, its amplitude gradually decreases with time because of friction. What happens to the period of the pendulum during this time? a) period increases b) period does not change c) period decreases ConcepTest 11.11 ConcepTest 11.11 Damped Pendulum

17. The period of a pendulum does not depend on its amplitudelength acceleration due to gravity The period of a pendulum does not depend on its amplitude, but only on its length and the acceleration due to gravity. g L T  22 After a pendulum starts swinging, its amplitude gradually decreases with time because of friction. What happens to the period of the pendulum during this time? a) period increases b) period does not change c) period decreases ConcepTest 11.11 ConcepTest 11.11 Damped Pendulum Follow-up: What is happening to the energy of the pendulum?

18. a) yes b) no c) it depends on the medium the wave is in ConcepTest 11.13Sound It Out ConcepTest 11.13 Sound It Out Does a longitudinal wave, such as a sound wave, have an amplitude ? low high normalairpressurex A

19. a) yes b) no c) 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 11.13Sound It Out ConcepTest 11.13 Sound It Out Does a longitudinal wave, such as a sound wave, have an amplitude ? low high normalairpressurex A

20. ConcepTest 11.16Out to Sea ConcepTest 11.16 Out to Sea t t +  t a) 1 second b) 2 seconds c) 4 seconds d) 8 seconds e) 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?

21. ConcepTest 11.16Out to Sea ConcepTest 11.16 Out to Sea t t +  t a) 1 second b) 2 seconds c) 4 seconds d) 8 seconds e) 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 !!

22. ConcepTest 11.19aStanding Waves I ConcepTest 11.19a 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: a b a) is zero everywhere b) is positive everywhere c) is negative everywhere d) depends on the position along the string

23. 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 11.19aStanding Waves I ConcepTest 11.19a 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: a) is zero everywhere b) is positive everywhere c) is negative everywhere d) depends on the position along the string

24. ConcepTest 12.1a ConcepTest 12.1a Sound Bite I a) the frequency f b) the wavelength c) the speed of the wave d) both f and e) both v wave and When a sound wave passes from air into water, what properties of the wave will change?

25. ConcepTest 12.1a ConcepTest 12.1a Sound Bite I a) the frequency f b) the wavelength c) the speed of the wave d) both f and e) 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?

26. Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day? a) more quickly on a hot day b) equal times on both days c) more quickly on a cold day ConcepTest 12.2b ConcepTest 12.2b Speed of Sound II

27. Do you expect an echo to return to you more quickly or less quickly on a hot day, as compared to a cold day? a) more quickly on a hot day b) equal times on both days c) more quickly on a cold day The speed of sound in a gas increases with temperature. This is because the molecules are bumping into each other faster and more often, so it is easier to propagate the compression wave (sound wave). ConcepTest 12.2b ConcepTest 12.2b Speed of Sound II

28. 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? a) drops to 1/2 its original value b) drops to 1/4 its original value c) drops to 1/8 its original value d) drops to 1/16 its original value e) does not change at all ConcepTest 12.4a ConcepTest 12.4a Sound Intensity I

29. 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? a) drops to 1/2 its original value b) drops to 1/4 its original value c) drops to 1/8 its original value d) drops to 1/16 its original value e) does not change at all distance doubles decrease to one-quarter Due to the inverse square law if the distance doubles, the intensity must decrease to one-quarter its original value. ConcepTest 12.4a ConcepTest 12.4a Sound Intensity I Follow-up: What distance would reduce the intensity by a factor of 100?

30. a)the long pipe b)the short pipe c)both have the same frequency d)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 12.6a ConcepTest 12.6a Pied Piper I

31. 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. a)the long pipe b)the short pipe c)both have the same frequency d)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 12.6a ConcepTest 12.6a Pied Piper I

32. 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? a) frequency will increase b) frequency will not change c) frequency will decrease ConcepTest 12.6c ConcepTest 12.6c Pied Piper III

33. 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? a) frequency will increase b) frequency will not change c) 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 12.6c ConcepTest 12.6c Pied Piper III Follow-up: Why doesn’t the wave speed change?

34. a)depends on the speed of sound in the pipe b)you hear the same frequency c)you hear a higher frequency d)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 12.7 ConcepTest 12.7 Open and Closed Pipes

35. 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. a)depends on the speed of sound in the pipe b)you hear the same frequency c)you hear a higher frequency d)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 12.7 ConcepTest 12.7 Open and Closed Pipes Follow-up: What would you have to do to the pipe to increase the frequency?

36. Speakers A and B emit sound waves of = 1 m, which interfere constructively at a donkey located far away (say, 200 m). What happens to the sound intensity if speaker A steps back 2.5 m? L A B a) intensity increases b) intensity stays the same c) intensity goes to zero d) impossible to tell ConcepTest 12.9 ConcepTest 12.9 Interference

37. = 1 m2.5 m2.5 out of phasedestructive interference If = 1 m, then a shift of 2.5 m corresponds to 2.5, which puts the two waves out of phase, leading to destructive interference. The sound intensity will therefore go to zero. Speakers A and B emit sound waves of = 1 m, which interfere constructively at a donkey located far away (say, 200 m). What happens to the sound intensity if speaker A steps back 2.5 m? L A B a) intensity increases b) intensity stays the same c) intensity goes to zero d) impossible to tell ConcepTest 12.9 ConcepTest 12.9 Interference Follow-up: What if you move back by 4 m?

38. a) pair 1 b) pair 2 c) same for both pairs d) 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 12.10 ConcepTest 12.10 Beats Pair 2 Pair 1

39. 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. a) pair 1 b) pair 2 c) same for both pairs d) 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 12.10 ConcepTest 12.10 Beats Pair 2 Pair 1

40. 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? a) frequency is highest at A b) frequency is highest at B c) frequency is highest at C d) frequency is the same at all three points ConcepTest 12.11a ConcepTest 12.11a Doppler Effect I

41. 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? a)frequency is highest at A b)frequency is highest at B c)frequency is highest at C d)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 12.11a ConcepTest 12.11a Doppler Effect I Follow-up: Where is the frequency lowest?

42. 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? a) lower than f 0 b) equal to f 0 c) higher than f 0 ConcepTest 12.11b ConcepTest 12.11b Doppler Effect II

43. 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? a) lower than f 0 b) equal to f 0 c) 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 12.11b ConcepTest 12.11b Doppler Effect II