Physics homework #09

1. A wave is described by y(x, t) = 0.48 sin(2.5πx − 4πt), in which all numerical constants are in the

SI units. Find the amplitude A, wavelength λ, frequency f and period T of this wave.

2. A piano tuner stretches a steel piano wire with a tension of 800 N. The steel wire is 0.4 m long and

has a mass of 3.0 g. (a) What is the frequency of its fundamental mode of vibration? (b) What
is the number of the highest harmonic that could be heard by a person who is capable of hearing
frequencies up to 10 kHz?

3. Consider an idealised model with a bird (treated as a point source) emitting constant sound power,

with intensity inversely proportional to the square of the distance from the bird. By how many
decibels does the sound intensity level drop when you move twice as far away from the bird?

4. Two submarines move head-on at 50 km/h and 70 km/h in a motionless water. The sound travels

at 5470 km/h. The first sub sends out a sonar signal at frequency 1000 Hz. What is the signal’s
frequency detected by the other sub?

5. Your clock radio awakens you with a steady and irritating sound of frequency 600 Hz. One morning,

it malfunctions and cannot be turned off. In frustration, you drop the clock radio out of your fourth-
story dorm window, 15.0 m from the ground. Assume the speed of sound is 343 m/s. As you listen
to the falling clock radio, what frequency do you hear just before you hear the radio striking the
ground?

6. A tuning fork vibrating at 512 Hz falls from rest and accelerates at 10 m/s

2

. (a) What is its velocity

and position when it emits sound recorded later at the release point as a wave having frequency
496 Hz? (b) How long after releasing the tuning fork waves of frequency 496 Hz reach the release
point? Take the speed of sound in air to be 310 m/s.

7. A supersonic jet travelling at Mach 3.00 at an altitude of

20 000 m is directly over a person at time t = 0 as in figure
below. (a) How long will it be before the person encounters
the shock wave? (b) Where will the plane be when it is finally
heard? (Assume the speed of sound in air is 335 m/s.)

8. A bat flies toward a wall, emitting a steady sound of frequency 2.0 kHz. This bat hears its own sound

plus the sound reflected by the wall. How fast should the bat fly in order to hear a beat frequency
of 10 Hz? (Hint: The wall first acts as a listener and then as a source.)

Maciej Wo loszyn

WFiIS AGH

http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/