The marine biologist measures the number of clicks per second to be 2437 Hz. The

Question

The marine biologist measures the number of clicks per second to be 2437 Hz. The dolphin is swimming away from the stationary marine biologist at vd = 8.30 m/s. The school of fish is swimming towards the dolphin. Their speed (with respect to the stationary biologist) is vf = 10.8 m/s.
a) What is the frequency of clicks produced by the dolphin? _______Hz
b) What frequency of clicks are detected by the school of fish? ______Hz
c) What frequency of clicks does the dolphin detect reflected from the marine biologist? ______Hz
d) What frequency of clicks does the dolphin detect reflected from the school of fish? _______Hz
e) What is the speed of the fish relative to the dolphin? _______m/s towards the dolphin

Explanation / Answer

(a) Here, the dolphin is swimming away from biologist. This means the frequency of the sound wave that is detected by the biologist is lower than the dolphin is emitting.

Therefore, use the following equation to determine the frequency that the dolphins are emitting.


f observed = [v/(v + vs] * f source

given that -

f observed = 2437 Hz, v = 1522 m/s, vs = 8.30 m/s

so -

2437 = [1522/(1522 + 8.3] * f source

=> f source = 2437 * (1530.3 / 1522) = 2450.3 Hz

Therefore, frequency of clicks produced by the dolphin = 2450.3 Hz

(b) Here the fish are swimming toward the dolphin, use the following equation to determine the frequency the fish heard.

f observed = [v/(v – vs] * f source

Since the dolphin is swimming away from the stationary marine biologist at 8.3 m/s, the dolphin is swimming toward the fish at 8.3 m/s. And the fish are swimming toward biologist at 10.8 m/s, the speed of the fish relative to the dolphin is (8.3 + 10.8) 19.1 m/s.

therefore, we have -

f observed = [1522/(1522 – 19.1] * 2437 * (1530.3 / 1522)

= [1522/(1502.9)] * 2437 * (1530.3 / 1522) = 2481.4 Hz

(c) Since the dolphin is swimming away from biologist, the frequency of clicks reflected from the marine biologist is less than 2450.3 Hz.

Use the following equation.

f observed = [v/(v + vs] * f source

f source = 2450.3 Hz

f observed = (1522/1530.3) * 2450.3 = 2437 Hz

So, the frequency of clicks does the dolphin detect reflected from the marine biologist = 2437 Hz

(d) Since the dolphin and fish are moving toward each other, the frequency dolphin detects reflected from the school of fish is the same as the fish detected means 2481.4 Hz.

(e) Speed of the fish relative to the dolphin = 8.30 + 10.8 =  19.10 m/s


2491.1113213 Hz

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