Problem 1 How long does it take for a pulse to travel the length of a 20m long a

Question

Problem 1 How long does it take for a pulse to travel the length of a 20m long aluminum wire with a 3mm diameter under a tension of 80N? The density (mass/volume) of aluminum is 2700 kg/m3.

Problem 2 A wave of the form: y(x,t) = 0.05m cos[ (2 m-1) x + (500 s-1) t ] travels down a string with a linear density of 3×10-4kg/m. (a) What is the speed and direction of the wave?

(b) What is the maximum speed of a point on the string as the wave passes?

(c) What is the average power transmitted down the string?

sound sProblem 3 A pipe, with one end open and one end closed, produces sound at a frequency of 132Hz. (a) What is the length of the pipe?

(b) What are the next two lowest harmonic frequencies (not including 132 Hz) produced by this pipe.

Problem 4 A guitar string has a linear density of 3×10-4 kg/m and a length of 0.6m. (a) What tension is needed to tune the string to have a fundamental frequency of 132 Hz?

(b) Suppose at the same tension in part (c), the string is held along a fret to make its length 0.4m. What are the 3 lowest frequencies now produced by this string?

Problem 5

(a) 4.5s after a supersonic jet passes directly overhead a sonic boom is heard. If the jet is moving at 450 m/s then what is its height? Assume the jet moves in a straight line at a constant altitude.

(b) A police car moves at 25m/s behind a speeder racing away from him at 40m/s. If the police car’s siren produces sound at a frequency of 710Hz, then what is the frequency heard by the speeder?

Problem 6 A speaker produces a spherical wave at a frequency of 132 Hz. 5m from the speaker the intensity is

8.0×10-5W/m2. (a) What is the total average power produced by the speaker?

(b) What is the sound level in dB at that 5m position?

(c) What are the displacement amplitude and pressure amplitude at that 5m position?

Explanation / Answer

The speed of propagation is sqrt(T/u) = sqrt( 32/12g/8m ) = 150 m/s

Using this, since it's 8m long, the total time it takes to travel is:
8m/(150m/s) = 53 ms ~= 54.8 ms

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