Question

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 temperature of water is 20 degrees C. Answer in cm

Answer 1

Answer: 14.82 cm

The speed
`v` 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`