Question

Sonar is used to determine the speed of an object. A 38.0-kHz signal is sent out, and a 40.0-kHz signal is returned. If the speed of sound is 341 m/s, how fast is the object moving?

Answer 1

The velocity is
`v = 8.743 \ m/s`

Step-by-step explanation:

From the question we are told that

The frequency of the signal sent out is
`f_s = 38.0 \ kHz = 38.0 *10^(3) \ Hz`

The frequency of the signal received is
`f_r = 40.0 \ kHz = 40.0 *10^(3) \ Hz`

The speed of sound is
`v_s = 341 \ m/s`

Generally the frequency of the sound received is mathematically represented as

`f_r = f_s [(v_s + v)/(v_s - v) ]`

where v is the velocity of the object

=>
`40 *10^(3) = 38 *10^(3) * [(341 + v)/(341 - v) ]`

=>
`1.05263 = (341+v )/(341-v)`

=>
`358.94 - 1.05263v = 341 + v`

=>
`17.947 = 2.05263 v`

=>
`v = 8.743 \ m/s`