Question

A sonar pulse has a wavelength of 3.0 cm. If the pulse has speed in water of 1,500 m/s, what is its frequency?

Answer 1

`5.0xx10^4color(white)(i)Hz`

Explanation:

The universal wave equation states that the velocity of a wave is the product of its wavelength and its frequency.

Mathematically speaking,

`color(blue)(|bar(ul(color(white)(a/a)v=lambdafcolor(white)(a/a)|)))`

`ul("where")`:
`v=`velocity of wave (metres per second)
`lambda=`wavelength (metres)
`f=`frequency (hertz or reciprocal seconds)

Step 1
Convert the given wavelength from centimetres into metres.

`3.0color(white)(i)cmxxm/(100color(white)(i)cm)`

`=3.0color(red)cancelcolor(black)(cm)xxm/(100color(red)cancelcolor(black)(cm))`

`=0.030color(white)(i)m`

Step 2
Rearrange for frequency, `f`, in the universal wave equation.

`v=lambdaf`

Becomes,

`f=v/lambda`

Step 3
Substitute your known values to solve for the frequency of the pulse.

`f=(1500color(white)(i)m/s)/(0.030color(white)(i)m)`

`f=50000color(white)(i)Hz`

Rounding off the value to two significant figures,

`f=color(green)(|bar(ul(color(white)(a/a)color(black)(5.0xx10^4color(white)(i)Hz)color(white)(a/a)|)))`