1.Two waves
travel on the same string. Is it possible for them to have (a) different
frequencies; (b) different wavelengths; (c) different speeds; (d) different
amplitudes; (e) the same frequency but different wavelengths? Explain your
reasoning.
2. Under a
tension F, it takes 2.00 s for
a pulse to travel the length of a taut wire. What tension is required (in terms
of F) forthe pulse to take 6.00 s instead?
3. What kinds
of energy are associated with waves on a stretched string? How could you detect
such energy experimentally?
4. The
amplitude of a wave decreases gradually as the wave travels down a long,
stretched string. What happens to the energyof the wave when this happens?
5. For the wave
motions discussed in this chapter, does the speed of propagation depend on the
amplitude? What makes you say this?
6. The speed of
ocean waves depends on the depth of the water; the deeper the water, the faster
the wave travels. Use this toexplain why ocean waves crest and
“break” as they near the shore
7. Is it
possible to have a longitudinal wave on a stretched string? Why or why not? Is
it possible to have a transverse Wave on
a steel rod? Again, why or why not? If your answer is yes in either case,
explain how you would create such a wave.
8. An echo is
sound reflected from a distant object, such as a wall or a cliff. Explain how
you can determine how far away theobject is by timing the echo.
9. Why do you
see lightning before you hear the thunder? A familiar rule of thumb is to start
counting slowly, once per second,when you see the lightning; when you hear the
thunder, divide the number you have reached by 3 to obtain your distance from
the lightning in kilometers (or divide by 5 to obtain your distance inmiles).
Why does this work, or does it?
10. For
transverse waves on a string, is the wave speed the same as the speed of any
part of the string? Explain the difference between these two speeds. Which one
is constant?
11. Children
make toy telephones by sticking each end of a long string through a hole in the
bottom of a paper cup and knotting it so it will not pull out. When the spring
is pulled taut, sound can be transmitted from one cup to the other. How does
this work? Why is the transmitted sound louder than the sound traveling through
air for the same distance?
12. The four
strings on a violin have different thicknesses, but are all under approximately
the same tension. Do waves travel faster on the thick strings or the thin
strings? Why? How does the fundamental vibration frequency compare for the
thick versus the thin strings?
13. A
sinusoidal wave can be described by a cosine function, which is negative just
as often as positive. So why isn’t the averagepower delivered by this wave
zero?
