Physics 102 Exam 2
SOLUTIONS
1 April 2005 Prof L. Weinstein

Please give a short explanation for all of your non-numerical answers (unless otherwise noted). Show your work for all numerical answers.

Useful numbers: Atmospheric pressure = $10^5$ Pa = 100,000 N/m$^2$

Absolute zero = 0 K = -273$^o$ C = -459$^o$ F

Density of water = 1000 kg/m$^3$

Density of air at room temperature = 1.2 kg/m$^3$

The speed of sound in air (at 20$^o$ C, 1 atmosphere) is $v = 340$ m/s

The speed of sound in water is $v = 1500$ m/s

Speed of light in vacuum $c = 3.0*10^8$ m/s

1. (no explanation needed) Two pendulums each consist of a 5-cm diameter ball suspended from a 1-m string of negligible mass. One ball has a mass of 1 kg and the other has a mass of 2 kg. Both are pulled back an identical distance and allowed to swing freely. Ignore air resistance. Which pendulum has a longer period?

   =1.2in

   

   1. the heavier (2 kg) one
   2. the lighter (1 kg) one
   3. both the same
   4. need more information

2. (no explanation needed) Two identical pendulums each consist of a 1-kg ball suspended from a 1-m string of negligible mass. One (A) is pulled back a short distance and the other (B) is pulled back a longer distance. Both are then allowed to swing freely. Ignore air resistance. Which pendulum has a longer period?

   =1.2in

   

   
   

   1. the short-distance one (A)
   2. the longer-distance one (B)
   3. both the same
   4. need more information

3. A mass is attached to a spring and oscillates up and down at a certain period $T$ and frequency $f$ . If I change the spring so that the period doubles, what is the new frequency of oscillation?
   1. ${1\over 4}f$
   2. ${1\over 2}f$ (correct answer)
   3. $f$
   4. $2f$
   5. $4f$
   6. need more information
   
   
   The period T = 1/f so if you double T, you halve f.
   
   
   
   

4. At a particular spot on the ocean, you notice that the waves are remarkably regular. You determine that the waves have a period of 2 s, a wavelength of 7 m, and an amplitude (height) of 0.3 m. What is the speed of the water wave?

   
   v = lambda * f = lambda / T = 7 m / 2 s = 3.5 m/s
   
   
   
   
   

5. In the previous problem, you watch the water at one particular point for 10 s starting from when the water is at its lowest point. How many wavecrests pass through that point in 10 s?

   In 10 sec, the wave goes through (10 s / 2 s) = 5 periods.  Therefore, 5 wavecrests pass you.
   
   
   
   
   
   

6. A small orchestra is playing music in a parade while riding on a truck. The violin plays an 'A' at 440 Hz while the truck is moving toward you. What frequency do you hear?
   1. lower pitched (less than 440 Hz)
   2. the same note (440 Hz)
   3. higher pitched (more than 440 Hz)
   4. need more information
   
   
   Doppler shift.  The source of the sound is moving towards you.
   
   
   
   

7. What is the wavelength of a 256 Hz sound in air?

   v = lambda * f therefore lambda = v / f = 340 m/s / 256 1/s = 1.33 m
   
   
   
   
   
   

8. How does the resonant frequency of a large (3-foot) bell compare to that of a small (3-inch) bell? The resonant frequency of the large bell is:
   1. much lower
   2. about the same
   3. much higher
   4. it depends on how you hit it
   5. need more information
   
   
   The lowest frequency standing wave on a large bell will have a much longer wavelength than that on a small bell since the wavelength is comparable to the size of the bell.  Longer wavelength <==> lower frequency.  Note that, if the bells are swinging, then the large bell will also swing with a lower frequency.  However, this has nothing to do with the resonant frequency (which is the sound you hear when you hit it with a hammer).
   
   
   
   

9. If I double the frequency of a sound wave, what happens to its wavelength?
   1. it quarters
   2. it halves
   3. it stays the same
   4. it doubles
   5. it quadruples
   6. need more information
   
   v = lambda * f <--> lambda = v / f.  Since the velocity of a sound wave is independent of frequency, if you double f, then lambda will get two times smaller.
   
   
   
   
   

10. You are in the space shuttle in orbit around the Earth when there is a large explosion about 1 mile (1.6 km) away. Which of the following is true?
    1. You hear the explosion before you see it
    2. You see the explosion before you hear it
    3. You see the explosion but you do not hear it
    4. You hear the explosion but you do not see it
    5. need more information
    
    Sound does not travel in vacuum.  You will not hear it.
    
    
    
    
    

11. A metal piano string vibrates in a standing wave. A snapshot of the piano strong at a particular instant is shown in the figure below. What is the wavelength of the wave?

     

    
    
    There are 5/2 wavelengths on the string, therefore 150 cm = 5/2 * lambda or lambda = 2/5 * 150 cm = 60 cm.
    
    
    
    

12. A metal piano string vibrates in a standing wave with a period of $T=0.01$ s. A snapshot of the piano string at the instant when the wave is at maximum displacement is shown in the figure below. Draw (on the same diagram) the pattern of the piano string half a period (ie: 0.005 s) later.

     

    
    
    
    In one period, the nodes do not move and the antinodes go from maximum upward displacement, through maximum downwards displacement and back to their original position (or down-up-down if they start in the maximum downward displacement).  Therefore, in half a period, the string goes from up to down or from down to up.  The dashed red curve shows where it will be 1/2 period later.
    
    
    

13. (no explanation needed) The background noise in a room is measured to be 50 dB. If the noise level doubles, the new measurement will be
    1. 25 dB
    2. 50 dB
    3. between 50 and 60 dB (60 dB would be ten times the noise level so the answer has to be between 50 and 60)
    4. 60 dB
    5. 100 dB
    6. need more information

14. Order the following from longest wavelength to shortest: middle C (sound at 256 Hz), x-rays, microwaves, blue light, red light.

    middle C has lambda = 1.3 m (from previous problem).  
    
    The electromagnetic waves are in this order: microwaves, red, blue, x-rays.  Since microwaves have lambda measured in cm, middle C comes before them.  Therefore we have:
    
    middle C, microwaves, red, blue, x-rays
    
    

15. You try to determine the color of an object by shining light at it. If you shine red light at it, it looks red. In green light it looks green. In blue light it looks black. What color is the object?

    It reflects red and green but absorbs blue.  Therefore it must be yellow. (yellow)
    
    
    
    
    
    

16. You shine cyan light on a magenta shirt. What color do you see?

    
    Incoming light = cyan = B + G
    Magenta shirt reflects R + B and it absorbs G.
    Therefore, we have (B+G) - G = B
    and the answer is BLUE
    
    

17. Some color-blind people only have cone cells that can detect red light and green light (ie: they have no blue-sensitive cone cells). If you show them a magenta shirt, what color will it appear to them?

    Magenta = R + B light hits them.  They do not see the blue light, only the red light.  Therefore they see red.