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

Answer

79.8 miles per hours fast is the car going.

Formula

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

$f_{observed} = f_{source}(\frac{v}{v - v_{source}} )$

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

$503.7= 450\times \frac{1100}{1100 - v_{source}}$

$503.7\times {1100 - v_{source}=450\times 1100$

$554070- 503.7v_{source}=495000$

$554070-495000=503.7v_{source}$

$59070=503.7v_{source}$

$v_{source}= \frac{59070}{503.7}$

$v_{source}= 117.3\ ft\ per\ s(Approx)$

Now convert 117.3 ft per second into miles per hours.

$1\ foot = \frac{1}{5280}\ miles$

$1\ hours = \frac{1}{3600}\ hours$

$\frac{117.3\ feet}{second} = \frac{117.3\times \frac{1}{5280}\ miles}{\frac{1}{3600}\ hours}$

$\frac{117.3\ feet}{second} = \frac{0.022216\ (Approx)}{0.00028\ (Approx)}$

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.