Question

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear

Answer 1

The values is
`f_b =14.9 \ beats/s`

Step-by-step explanation:

From the question we are told that

The speed of the fire engine is
`v = 5\ m/s`

The frequency of the tone is
`f = 500 \ Hz`

The speed of sound in air is
`v_s = 340 \ m/s`

The beat frequency is mathematically represented as

`f_b = f_a - f`

Where
`f_a` is the frequency of sound heard by the people in the fire engine and is is mathematically evaluated as

`f_a = [(v_s + v )/(v_s -v) ]* f`

substituting values

`f_a = [(340 + 5 )/(340 -5) ]* 500`

`f_a = 514.9 \ Hz`

Thus

`f_b =514.9 - 500`

`f_b =14.9 \ beats/s`