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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

Verified Answer :

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.

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