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PHYSICS

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Summer 201

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Homework #6 Due Friday
July 26, 2013

1. Assume four objects each of mass m are placed at the corners of a square of side length a. How much
work needde to separate the planets so that they are infinitely away from each other?

2. A block of mass m = 1.

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0 kg oscillates in simple harmonic motion due to the force of the spring to which
the block is attached to. The amplitude of motion is A = 0.14 m and the maximum speed of the block is
vm = 2.30 m/s.

(a) What is the spring constant of the spring?

(b) Express the displacement of the spring in terms of A when v =
vm
2

and find its value.

(c) Express the speed of the block in terms of vm when the displacement is x =
A

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3. The suspension system of your 1200 kg car has a natural oscillation frequency of 2.00 Hz without func-
tioning shock absorbers. The shock absorbers provide critical damping to the system. Along a worn
section of concrete highway you notice concrete joints spaced 10.0 m apart setup a violent oscillation of
the car. At what speed are you driving?

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PHYSICS 221
Summer 2013

Homework #6 Due Friday
July 26, 2013

4. What is the percentage change in the frequency of a pendulum’s simple harmonic motion if its length is
increased by 0.10%?

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. A sinusoidal transverse wave moves along a stretched string in the +̂ direction with amplitude 5.00 cm,
wavelength 2.00 m, and wave speed 200 m/s. The particles in the string oscillate along the z axis.

(a) What are the wave number, frequency and angular frequency of the wave?

(b) Write a possible wave function for the wave with an explanation.

(c) If the tension in the string is 50.0 N, what is the linear mass density of the string?

(d) How much average power is transmitted along the string?

(e) What would the wave function be in (b) if the wave traveled in the −̂ direction?

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PHYSICS 221
Summer 2013
Homework #6 Due Friday
July 26, 2013

6. A car chases a coyote down a road ending in a sheer cliff. The car has a speed of 40.0 m/s and the coyote
has a speed of 30.0 m/s. The car blows a siren at 440 Hz and the speed of sound is 340 m/s.

(a) What frequency does the coyote hear for the sound coming directly from the car?

(b) What frequency does the coyote hear for the sound reflected from the cliff?

(c) What beat frequencies do do each the coyote and driver hear?

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PHYSICS 221
Summer 2013
Homework #6 Due Friday
July 26, 2013

7. The second harmonic sinusoidal standing wave in a pipe with both ends open has a wavelength of 2.00 m.
The sound speed is 340 m/s

(a) How many nodes and anti-nodes are there in the displacement wave? How many nodes are there in
the pressure wave? Draw the positions of these nodes and anti-nodes.

(b) What is the length of the pipe?

(c) What is the frequency of the second harmonic?

(d) What is the frequency of the fundamental mode in this pipe?

(e) If the same pipe was closed at one end and open at the other what would be the frequency of the
fundamental mode and the third harmonic?

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PHYSICS 221
Summer 2013
Homework #6 Due Friday
July 26, 2013

8. The source of a point source of delivers 1.00 µW of sound power.

(a) What is its intensity 3 m away?

(b) What is the sound level in dB 3.00 m away?

(c) What is the sound level in dB 6.00 m away?

9. By what factor should the sound intensity be increased to

(a) increase the sound intensity level by 10 dB?

(b) increase the sound intensity level by 20 dB?

(c) increase the sound intensity level by 23 dB?

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