A whale uses sonar (sound waves) to supplement its eyesight for deep water dives

Question

A whale uses sonar (sound waves) to supplement its eyesight for deep water dives. If the speed of sound in water is approximately 1500 m/s, interpret the following signals (as a whale's brain has evolved to do). You may assume the whale is at rest with respect to the water.

a.) The whale sends out a sound wave, which returns in 0.5 seconds. How far away is the object it bounced off?____m

b.) This sound wave arrives back with its frequency Doppler shifted upwards by 3%. How fast is this object moving towards the whale?____m/s

Explanation / Answer

(a) s = ut = 1500 * 0.5 = 750 m ; Therefore the distance traveled by the wave in 0.5 seconds to reach the object and come back is 750 ; therefore the distance between whale and the object it bounced off is 750 / 2 = 375 (b)let Velocity of object w.r.t whale V and c be the speen of light. Given F - f/F = 0.03 ==>V/c = 0.03 ==> V = 0.03 c = 9 x 10^6 m/sec

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