Question

A car approaches you with its horn blowing. The observed frequency is 503.7 Hz. Assume the speed of sound is 1100 ft/s. The car's horn has a frequency of 450 Hz. How fast is the car going? Express your answer in mph.

1420

79.8

117

Answer 1

79.8 miles per hours fast is the car going.

Formula

By using the dopplers effect. (When source is approching .)

`f_(observed) = f_(source)((v)/(v - v_(source)) )`

As given

A car approaches you with its horn blowing.

The observed frequency is 503.7 Hz.

The speed of sound is 1100 ft/s .

The car's horn has a frequency of 450 Hz.

i.e

`f_(observed) = 503.7 Hz`

v = 1100 ft/s

`f_(source) = 450 Hz`

Put in the above formula

`503.7= 450* (1100)/(1100 - v_(source))`

`503.7* {1100 - v_(source)=450* 1100`

`554070- 503.7v_(source)=495000`

`554070-495000=503.7v_(source)`

`59070=503.7v_(source)`

`v_(source)= (59070)/(503.7)`

`v_(source)= 117.3\ ft\ per\ s(Approx)`

Now convert 117.3 ft per second into miles per hours.

`1\ foot = (1)/(5280)\ miles`

`1\ hours = (1)/(3600)\ hours`

`(117.3\ feet)/(second) = (117.3* (1)/(5280)\ miles)/((1)/(3600)\ hours)`

`(117.3\ feet)/(second) = (0.022216\ (Approx))/(0.00028\ (Approx))`

117.3 feet per second = 79.8 miles per hours (Approx)

Thus

`v_(source)= 79.8\ miles\ per\ hours`

Therefore the 79.8 miles per hours fast is the car going.