A dolphin is able to tell in the dark that the ultrasound echoes received from two sharks come from two different objects only if the sharks are separated by 3.70 meters, one being that much farther away than the other. (a) If the ultrasound has a frequency of 115 kHz, show this ability is not limited by its wavelength. m < 3.50 m (b) If this ability is due to the dolphin's ability to detect the arrival times of echoes, what is the minimum time difference (in ms) the dolphin can perceive?

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A dolphin is able to tell in the dark that the ultrasound echoes received from two sharks come from two different objects only if the sharks are separated by 3.70 meters, one being that
much farther away than the other.
(a) If the ultrasound has a frequency of 115 kHz, show this ability is not limited by its wavelength.
m < 3.50 m
(b) If this ability is due to the dolphin's ability to detect the arrival times of echoes, what is the minimum time difference (in ms) the dolphin can perceive?
ms
Transcribed Image Text:A dolphin is able to tell in the dark that the ultrasound echoes received from two sharks come from two different objects only if the sharks are separated by 3.70 meters, one being that much farther away than the other. (a) If the ultrasound has a frequency of 115 kHz, show this ability is not limited by its wavelength. m < 3.50 m (b) If this ability is due to the dolphin's ability to detect the arrival times of echoes, what is the minimum time difference (in ms) the dolphin can perceive? ms
Expert Solution
Step 1

Part (b)

Given:

  • The distance between objects is d=3.70 m.
  • The frequency of ultrasound wave is f=115 kHz.

The formula to calculate the minimum time difference for which dolphin detect the echo is,

t=2dv

Here, t is the time difference of echo, 2d is the total distance covered by wave and v is the speed of sound in human.

The speed of sound in human tissue is v=1540 m/s.

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