Problem Set #1: Harmonic Motion and Sound Waves

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In summary, the conversation covered various problems and calculations related to simple harmonic motion, standing waves, tuning forks, and sound waves. The summary includes solutions for finding the mass, period, and acceleration of a block attached to a spring, the minimum frequency for setting up a standing wave on a wire, and the displacement of a string when the transverse speed first equals one-half of the maximum transverse speed. It also includes the equations and calculations for finding the frequency of a tuning fork, the maximum and minimum frequencies heard by a listener, the distance from a point source for a certain loudness, and the length of two organ pipes. Lastly, it discusses the solution for correcting the time on a grandfather clock by lengthening the pendulum.
  • #1
Shackleford
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I am not certain about 4.b, 5, and 6. Thanks for any help.

1. A block of unknown mass is attached to a spring with a force constant
of 6.50 N/m and undergoes simple harmonic motion with an amplitude of
10.0 cm. When the block is halfway between its equilibrium position
and the end point, its speed is measured to be 30 cm/s. Calculate a)
the mass of the block, b) the period of the motion, and c) the
maximum acceleration of the block. a) .541 kg b) 1.81 s c) 1.20 m/s

2. A student wants to establish a standing wave on a wire that is 1.80 m
long and clamped at both ends. The wave speed is 540 m/s. What is the
minimum frequency the student should apply to set up a standing wave?
150 Hz

3. A violin string has a length of 0.350 m and is tuned to concert G,
with f=392 Hz. Where must the violinist place her finger to play
concert A, with f=440 Hz? l = .311 m .039 m from end

4. A student holds a tuning fork oscillating at 256 Hz. He walks toward
a wall at a constant speed of 1.33 m/s. (a) What beat frequency does
he observe between the tuning fork and its echo? (b) How fast must he
walk away from the wall to observe a beat frequency of 5.00 Hz?
a) 1.9 Hz b) 3.31 m/s

There is a double Doppler shift in both situations. f1 (original source), f2, and f3.
For b), I set f3 = 261 and came up with two equations in terms of f2 and v. I setup a ratio and solved for v = 3.31 m/s


5. The equation of a harmonic wave on a string is given by
y=(3cm)sin(2x-5t) where x is in cm and t in seconds. Find the
displacement of the string when the transverse speed first equals
one-half of the maximum transverse speed. x = 1.0472

transverse speed = partial of y with respect to t = Yt = -.15 cos(2x-5t)
maximum transverse speed occurs when cosine equals +/-1 = .15 m/s
one-half of maximum transverse speed is .075 m/s
.075 m/s = Yt = -.15 cos(2x-5t)
-.5 = (2x-5t)
If I set t = 0, I get x = 1.0472


6. A tuning fork is heard to resonate over a resonance tube when the
air column is 48.5 cm long and again when it is 68.7 cm long. What is
the frequency of the tuning fork if the temperature is 26˚C? I couldn't figure out how to work this

7. A whistle of frequency 500 Hz moves in a circle of radius 1 m at
3 rev/s. What are the maximum and minimum frequencies heard by a
stationary listener in the plane of the circle and 5 m from its
center? 473.95 Hz, 529 Hz

8. A point source radiates sound uniformly in all directions. At a
distance of 10 m, the sound has a loudness of 80 dB. At what distance
from the source is the loudness 60 dB? What power is radiated by this
source? radius = 100 m, average power = .125

9. Organ pipe A, with both ends open, has a fundamental frequency of
300 Hz. The third harmonic of organ pipe B, with one end open, has
the same frequency as the second harmonic pf pipe A. How long is pipe
A and pipe B? A = .5716 m, B = .8575 m

10. In a grandfather clock, the pendulum measures the time elapsed. A
grandfather clock is gaining time. Should you shorten or lengthen
the pendulum in order to correct the time? Explain. Period needs to increase. Should lengthen pendulum.
 
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  • #2
Help?
 
  • #3
Please?
 
  • #4
ttt...
 
  • #5
Once again.
 
  • #6
vmax = wA = 5/s * 3 cm = 15 cm/s

y = A sin (kx - wt)

dy/dt = -5 * 3 cos(kx - wt) = -15 cos(2x - 5t) maximum value occurs when cosine equals +/-1

7.5 cm/s = -15 cos(2x - 5t)

2.0944 = cos(2x - 5t)

if x = 0, 2.0944 = -5t

t = -.4188

y = 3 sin(0 - 5(-.4188)) = 2.59 cm
 

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