Echolocation Dolphins utilize echolocation for navigation and targeting prey. Th

Question

Echolocation Dolphins utilize echolocation for navigation and targeting prey. The figure above shows a CT scan of a dolphin head showing the region where the bio-acoustic signal is generated. The signals emitted by many dolphins are whistles and brief broadband clicks. The right side of the above figure shows the temporal signal and its corresponding spectrum. The average duration for one of these pulses is 55 mu s and contains approximately 4.1timesl0-4 J of energy. Consider a bottlenose dolphin swimming in the Atlantic Ocean at a speed of 7 km/h towards a school of anchovy moving away from the dolphin at 0.3 m/s. What is the frequency observed at the anchovy school for the peak frequency (110 kHz) of the emitted echolocation click? Assume that the bio-acoustic emission from the dolphin is contained within a cone having an angular width of 10 degree. If the school of anchovy were 10 m from the dolphin, what is the intensity of the signal at the fish? Bats also use echolocation to navigate and track prey. However, a brown bat's bio-acoustic pulse is, on average, 22 ms long at distance and can shorten to about 0.5 ms during it's final attack. These are considerably longer than the pulse width emitted by dolphins. Hypothesize why this may be the case.

Explanation / Answer

I will just answer the physics part of this question.

This states that the frequency emitted by the source(dolphins) is 110kHz

We want to find the observed frequency.

We'll use the Doppler's formula (http://en.wikipedia.org/wiki/Doppler_effect):

f = f0 (c+vr)/(c+vs)

=> f = 110 x 103 (1500 + 1.94)/(1500 + 0.3) [ since 7 KM/H = 1.94 m/s][and speed of sound in water=1500]

=> f = 110.12 kHz

However for the case of air, f = 110.53KHz

Second part:

Now as given sound energy is 4.1 x 10-4 J in 55s.

So Sound Power is 4.1 x 10-4 J / 55s. = 7.4 Watts = P(say)

Thus intensity at 10 m will be I = P / 4r2 = 5.93x10-3

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Hope this helps.

Please rate.

Cheers.

:)

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