Question

Dolphins of the open ocean are classified as Type II Odontocetes (toothed whales). These animals use ultrasonic "clicks" with a frequency of 55 kHz to navigate and find prey. (a) Suppose a dolphin sends out a series of clicks that are reflected back from the bottom of the ocean 75 m below. How much time elapses before the dolphin hears the echoes of the clicks? (The speed of sound in seawater is approximately 1530 m/s.) (b) What is the wavelength of a 55-kHz sound in the ocean?

Solution

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The sound wave must travel back and forth (twice the depth).

Calculate the time by dividing the distance by the speed of sound.

$t=\dfrac{2d}{v}=\dfrac{2(75)}{1530\;m/s}=0.098\;s$

Now use the formula $v=\lambda f$

$\lambda=\dfrac{v}{f}=\dfrac{1530\;m/s}{55\times10^3\;Hz}=28\times10^{-3}\;m=28\;mm$

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