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

Question

asked Jul 4, 2020 15.1k views

1 Answer

Jakuje · Answer 1 · 2020-07-09T04:03:55+0000

The speed
of a wave (the sound in this case) is given by the following formula:

$v=f.\lambda$ (1)

Where:

f=100kHz=100(10)^(3)Hz is the frequency

$\lambda$ the wavelength

It is known that the speed of sound in water at
$20\ºC$ is:

v=1482(m)/(s)

So, we only have to find
$\lambda$ from (1):

$\lambda=(v)/(f)$ (2)

$\lambda=(1482(m)/(s))/(100(10)^(3)Hz)$

Knowing
1Hz=(1)/(s) :

$\lambda=0.01482m$

But we were asked to find the wavelength in cm and we have to make the conversion:

$\lambda=0.01482m.(100cm)/(1m)=14.82cm$

Hence:

$\lambda=14.82cm$