Physics 102
First Exam
Solutions
Oct 14, 2003
Instructions: The exam consists of two parts. Part I is multiple choice and is to be answered on the "scantron" sheet. On the name part of that sheet, please give (via filled circles) you last name first. Part II asks for drawing and short answers. Please put your name (via legible handwriting) on that sheet also, and copy and sign the pledge there (it will of course apply to the entire exam).
Handing in the exam: Put your scantron sheet in one tray,designated Part I. Put Part II detached from the rest of the exam, in the other tray. You may keep the questions of Part I as a precious souvenir, or recycle them.
The exam lasts one hour, with an extra 15 minutes for distribution, filling in names and pledges, and handing in of answers. All exams should be handed in by 10:45. Many of you will finish early, after handing in your answers you may then leave the lecture hall.

Part I   Answer on the NCS answer sheet.

Correct answers are in bold face.

1. "Kilohertz" (kHz) means
A.   (1/1000) Hz           B.   1000 kilocycles per second          C.   1000 Hz           D.   1 kg/sec  
 
2. A relation between period and frequency is
A.   all of the following (B-D)          B.   f = 1/T          C.   T = 1/f          D.   fT=1

3. The period of an audio-frequency tone is 0.5 ms. Its frequency is therefore
A.   50 Hz       B.   200 Hz       C.   500 Hz       D.   2000 Hz       E.   5000 Hz

4. The relationship between frequency and period holds
  1. for all types of waves       
  2. only for sound waves       
  3. only for sine waves       
  4. only for standing waves       
  5. only for longitudinal waves.
The diagram on the right is a plot of the motion of a mass that is bobbing up and down on a spring. The vertical scale shows the mass's height above the floor, and the horizontal scale shows time. Only part of the motion, starting at 5 sec, is shown. Use this plot to answer questions 5-8.
5. This motion is
A. not periodic              B. periodic but not simple harmonic       C. simple harmonic       
D. none of the above
 
6. How many periods are shown?
A.   one          B.   two          C.   three          D.   four

7. What is the period?
A.   1 sec          B.   2 sec          C.   4 sec         D.   7 sec         E.   9 sec

8. What is the amplitude?
A.   1 cm          B.   1.5 cm          C.   2 cm          D.   2.5 cm         E.   4 cm

9. How are SHM and uniform circular motion related?
  1. They are identical
  2. SHM is the projection of uniform circular motion.
  3. Uniform circular motion is the projection of SHM.
  4. Both have constant speed
  5. There is no simple relation between the two.
10. How are frequency and amplitude of a sine wave related?
  1. The higher the frequency, the larger the amplitude.
  2. The higher the frequency, the smaller the amplitude.
  3. The two add if the phase is zero, and subtract if the phase is 180°.
  4. The ratio of amplitude to frequency is proportional to the phase.
  5. There is no relation between the two, they are independent properties of the wave.

11. The perceived pitch of a sound wave is correlated to its
A.  amplitude         B.   frequency         C.   wave shape        D.   phase         E.  speed

12. The perceived loudness of a sound wave is correlated to its
A.  amplitude         B.   frequency         C.   wave shape        D.   phase         E.  speed

13. The perceived tone quality of a sound wave is correlated to its
A.  amplitude         B.   frequency         C.   wave shape        D.   phase         E.  speed

14. When two sine waves of equal frequency are displayed as a Lissajous figure (one wave on the x-axis, the other on the y-axis), the figure is a straight line. What can one say about the relation between the two waves?
  1. They have equal amplitudes
  2. They are either exactly in phase or exactly out of phase
  3. The phase difference between them is 90°
  4. The phase difference between them is 45°
  5. The phase difference between them equals the slope of the line.

15. Suppose the planet Mars blows up. About how long will it take before we hear the explosion?
A. a few seconds       B. a few hours       C. a few days     D. a few weeks        E. we will never hear it

16. A snapshot of a wave at one moment of time is shown on the right. As time goes on, the wave will be
  1. a propagating wave to the right
  2. a propagating wave to the left
  3. a standing wave of amplitude as shown in the snapshot
  4. a standing wave of amplitude different from that shown in the snapshot
  5. all of the above are possible, from the snapshot we cannot tell which applies.
17. The speed of sound in air depends on
  1. the amplitude of the sound wave
  2. the wave's frequency    
  3. the wave's period    
  4. the wave's intensity    
  5. the air temperature

18. On a cool day the echo from a wall half a kilometer distant took 3 seconds to return. The speed of sound that day was
A.  300 m/s       B.  333 m/s       C.  345 m/s       D.  350 m/s       E.  0.5 km/s

19. When a sound wave goes from air into another medium, some of it is transmitted and some is reflected. What feature of the transmitted wave is always the same as that of the original (incident) wave:
A.   wavelength       B.   frequency       C.   speed       D.   amplitude       E.    intensity

20. In a certain metal, sound waves with a frequency of 3000 Hz have a wavelength of 2 m. What is the speed of sound in this metal?
A.   345 m/s       B.   690 m/s      C.   1500 m/s         D.   3000 m/s       E.    6000 m/s

21. In a lecture experiment, we listened to a small unmouted speaker and compared its sound with that when a baffle was attached to the speaker. When there was no baffle, sound waves from the back of the speaker could propagate in the same (forward) direction as waves from the front of the speaker. The wave property that allowed waves from the back to bend around toward the front is called
A.   refraction       B.   diffraction       C.   deflection       D.   construction       E.   interference

22. In the experiment of the previous question, the wave property that allowed the waves from the front and back of the speaker to cancel at the location of the listener is called
A.   refraction       B.   diffraction       C.   deflection       D.   construction       E.   interference

23. When two sine waves that are 180° out of phase are added together, the amplitude of the sum is
  1. always zero       
  2. always less than the amplitude of either wave
  3. equal to the amplitude of the smaller wave       
  4. always less than the amplitude of the larger wave
  5. always greater than the amplitude of the smaller wave.
24. When you add two waves, each of amplitude A but of slightly different frequency, the result is
  1. a wave whose amplitude varies in time between 2A and 0
  2. alternating constructive and destructive interference between the waves
  3. a fluctuation of intensity of the sum wave at the difference frequency
  4. a phenomenon known as beats
  5. all of the above
25. When a sine wave of amplitude 2 V and period 8 ms is added to a sine wave of amplitude 1 V and period 4 ms, the result is
  1. a sine wave of amplitude 3 V
  2. a sine wave of amplitude 1 V
  3. a sine wave of period 6 ms
  4. a wave shape different from a sine wave
  5. none of the above
26. An electric bell is operating in a vacuum. We cannot hear the sound of the bell because
  1. air is needed to conduct the electric current to the bell
  2. the bell's metal cannot vibrate in vacuum
  3. there is no air to conduct the vibrations from the bell to our ears
  4. the vacuum jar absorbs the sound
  5. the noise of the pump is louder than the noise of the bell
27. Two sine waves are propagating in air. Wave 1 has twice the wavelength of wave 2. Therefore
  1. wave 1 has twice the frequency of wave 2
  2. wave 2 has twice the frequency of wave 1
  3. wave 1 has twice the amplitude of wave 2
  4. wave 1 has twice the speed of wave 2
  5. the two waves are always out of phase.

28. A triangle wave and a square wave can not have the same
A.  frequency        B.  amplitude        C.  phase        D.  tone quality        E.  speed

29. When the air in a tube is replaced by another gas, the fundamental vibration frequency increases by 50%. The speed of sound in the gas, compared to that of air, is
A.  half       B.  50% lower        C.  50% higher        D.  twice        E.  none of these

30. A rocket is launched and very quickly reaches supersonic speed. Where can the sonic boom be heard?
  1. at the launching pad
  2. in a plane flying directly overhead
  3. in a plane at the same distance above the ground as the rocket
  4. at many places on the ground, away from the launching pad
  5. all of the above.
31. A moving locomotive is sounding its horn as it crosses a highway. There are people in all directions from the locomotive -- in front, in back, to the right and left. Compared to the "true" pitch, as heard by the engineer, the horn's pitch heard by these people is
  1. higher       
  2. lower       
  3. the same for all of the people
  4. higher for some, true for others, and lower for yet others of the people

32. Which concept does not apply to ultrasonic waves:
A.  frequency     B.  intensity     C.  loudness     D.  speed     E.  wavelength

33. What is true about nodes of a standing wave on a string or in a tube:
  1. nodes are locations where the wave displacement is zero for all times
  2. the distance between nodes is half a wavelength
  3. between any pair of nodes there is an antinode
  4. a vibrating stretched rope with fixed ends has nodes at the ends
  5. all of the above

34. If the simplest standing wave in a rope has a frequency of 100 Hz when vibrating in one loop, at what frequency will the rope vibrate in two loops?
A.  25Hz       B.  50 Hz       C.  100 Hz       D.  200 Hz       E.  400 Hz

35. A tube open at both ends has a fundamental frequency of 100 Hz. The speed of sound inside the tube is 340 m/s. How long is the tube?
A.  0.85 m       B.  1.00 m       C.  1.70 m       D.  3.40 m       E.  3400 m

36.1  In the figure above, draw a distance that shows one wavelength. Label it l. (Thus: ¬l®)

37. If the frequency of the wave shown in the above figure is 500 Hz, what should be the time label at the end of the wave (where the arrow is)? Your answer should be a number with units, such as ms.

period = 1/f = (1/500) sec = 2 ms. The arrow is at the end of 3 periods, so the label should be 6 ms

38. On the same figure, above, draw exactly two periods of a square wave having twice the amplitude and half the wavelength of the wave that is already drawn.

39. Describe some experiment that demonstrates interference, as discussed in the text and/or shown in lecture. Write about 3 sentences,for example: one sentence for the set-up, one sentence what the effect is, one sentence why it shows interference.

Possible answers are Quincke's tubes, Young's experiment, phase reversal, speaker with baffle and others

40. The figures below represent a ``closed" tube (closed at one end). Draw the vibration pattern for the lowest two standing sound waves, in transverse representation. Label the nodes (N) and antinodes (A).

1each of these problems counts 3 points