Physics tutorial #12

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. On December 26, 2004, a great earthquake occurred off the coat of Sumatra and triggered immense

waves (tsunami). Satellites observing these waves from space measured 800 km from one wave crest
to the next and a period between waves of 1 hour. What was the speed of these waves in m/s and
km/h ? Does your answer help you to understand why the waves caused such devastation?

3. 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?

4. The B-string of a guitar is made of steel (density 7800 kg/m

3

), is 63.5 cm long, and has diameter

0.406 mm. The fundamental frequency is f = 247 Hz. (a) Find the string tension. (b) If the tension
F is changed by a small amount ∆F , the frequency f changes by a small amount ∆f . Show that

∆f

f

=

1
2

∆F

F

.

5. Show that the sound velocity in hydrogen is four times larger than the sound velocity in oxygen.

6. 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?

7. 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?

8. 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. (a) As you
listen to the falling clock radio, what frequency do you hear just before you hear the radio striking
the ground? (b) At what rate does the frequency that you hear change with time just before you
hear the radio striking the ground?

9. The weather radar operates at a frequency of 2.7 GHz. If a radar wave reflects from an approaching

weather system moving with a speed of 28 m/s, find the difference in frequency between the outgoing
and returning waves.

10. The loop of a circus ringmasters whip travels at Mach 1.38. What angle does the shock wave make

with the direction of the whips motion?

11. 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.)

12. 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?

Nivas Babu Selvaraj, Maciej Wo loszyn
http://fatcat.ftj.agh.edu.pl/~woloszyn/phys/