A whale uses sonar (sound waves) to supplement its eyesight. The whale swims in

Question

A whale uses sonar (sound waves) to supplement its eyesight. The whale swims in water where the speed of sound is measured to be 1458 m/s, and stays at rest with respect to the water.

Sensory input:
The whale can determine the location and speed of another object in the water, by sending out a sound wave towards it.

a.) The sound returns in 0.7 seconds. How far away is the object it bounced off?
_?_ m

b.) The wave arrives back with its frequency Doppler shifted upwards by 2%. How fast is this object moving and in what direction?
_?_ m/s, towards /away from /neither towards nor away from? the whale

Assuming the object continues with its current velocity, how much time until it arrives at the whale?
_?_ s

The environment:
c.) Dissolving salt into water will increase its density. Conceptually, this factor alone would tend to increase/decrease N/A: no effect? the speed of sound, compared to in fresh water.

d.) Assuming salt water and fresh water have the samea bulk modulus, find how much salt is dissolved into a 1 m3 block of this particularb sea water.
_?_ kg

(aNote: this is NOT a good assumption-- it is actually affected MORE by the added salt than density is!)

(bNote: Salinity varies in different parts of the world's oceans.)

Explanation / Answer

a)
Distance = velocity *time = 1458*0.7/2 = 510.3 m
b)
The object perceives a frequency N’ and
N’ / N = (C + v) / C

The whale perceives a frequency N” and
N”/ N’ = C /(C- v)

On multiplying the two


N”/N = (C + v) / (C-v) = 1.02 (given 2% increase)

(1458 +v) / (1458 –v) = 1.2

v = 132.540 m/s

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