A dolphin emits ultrasound at 100 kHz and uses the timing of reflections to determine the position of objects in the water. What is the wavelength of this ultrasound?

Answer :

Explanation:

It is known that speed of sound in water at a temperature of [tex]20^{o}C[/tex] is 1482 m/s.

And, formula showing relation between wavelength, velocity and frequency is as follows.

           [tex]\lambda = \frac{\nu}{f}[/tex]

where,      [tex]\lambda[/tex] = wavelength

                [tex]\nu[/tex] = velocity

                     f = frequency

Putting the given values into the above formula as follows.

           [tex]\lambda = \frac{\nu}{f}[/tex]

                       = [tex]\frac{1482 m/s}{100 kHz}[/tex]

                       = [tex]\frac{1482 m/s}{100000 Hz}[/tex]       (as 1 kHz = 1000 Hz)

                       = 0.01482 m

thus, we can conclude that the wavelength of this ultrasound is 0.01482 m.

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