Travelling Wave in a String:
We are observing a string whose transverse displacement y
is given [in
units] as a function of time t
and position z (down the length of the string) by
(a)
In what direction is the wave traveling?
(b)
What is the amplitude of the traveling wave?
(c)
What is the frequency of
at any point on the string?
(d)
What is the wave propagation velocity on the string?
2.
Power in a Wavy String:
If a continuous transverse sinusoidal wave of amplitude A
is propagating down a taut string of linear mass density
at velocity v with frequency ,
show that the
power transmitted in the wave is
.
3.
Double Doppler Effect:
Sound waves are emitted by a source moving at vs
directly toward a detector which in turn is moving
directly toward the source at a speed vd.
Both vs and vd are less than the speed of sound c.
If
is the frequency at which the sound is emitted
in the rest frame of the source, show that
the frequency f which is detected by the moving detector
is given by
.