Doppler Effect Problems

1. One end of stationary rope is tied to a support at the end of a vertical mine shaft 800m deep, the other end is fixed at the bottom by means of a 20kg weight. If a man at the bottom of the shaft signals to someone at the top by jerking the rope sideways, how long will it take for this signal to travel from bottom to top of the shaft? The velocity of wave propagation in a stretched string is c = sqrt(T/p), where T is the tension and p (rho) is the mass per unit length of the string.

2. A stretched wire gives a beat frequency of 2 beats per second when sounded with a tuning fork when its length is 1.43 and when its length is 1.45 m, the tension on the wire remaining constant throughout. What is the frequency of the tuning fork?

3. A major device used by naval vessels to detect submarines is SONAR. A sonar set consists of a sound source and a sensitive microphone, both placed below the waterline. The source emits short bursts of sound and microphone detects any sound that is reflected back. The time internal between emission and detection can be used to find the distance to the reflection object.

Suppose a destroyer is moving due west at 9.5m/s with respect to the ocean bottom, an ocean current moves due east at 1.3m/s. If a submarine is heading due east, directly towards the destroyer, at 14m/s, what is the value of the observed Doppler shift? The source frequency is 8kHz, speed of sound in sea water is 1470m/s.