Respuesta :
Answer
79.8 miles per hours fast is the car going.
Formula
By using the dopplers effect. (When source is approching .)
[tex]f_{observed} = f_{source}(\frac{v}{v - v_{source}} )[/tex]
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
[tex]f_{observed} = 503.7 Hz[/tex]
v = 1100 ft/s
[tex]f_{source} = 450 Hz[/tex]
Put in the above formula
[tex]503.7= 450\times \frac{1100}{1100 - v_{source}}[/tex]
[tex]503.7\times {1100 - v_{source}=450\times 1100[/tex]
[tex]554070- 503.7v_{source}=495000[/tex]
[tex]554070-495000=503.7v_{source}[/tex]
[tex]59070=503.7v_{source}[/tex]
[tex]v_{source}= \frac{59070}{503.7}[/tex]
[tex]v_{source}= 117.3\ ft\ per\ s(Approx)[/tex]
Now convert 117.3 ft per second into miles per hours.
[tex]1\ foot = \frac{1}{5280}\ miles[/tex]
[tex]1\ hours = \frac{1}{3600}\ hours[/tex]
[tex]\frac{117.3\ feet}{second} = \frac{117.3\times \frac{1}{5280}\ miles}{\frac{1}{3600}\ hours}[/tex]
[tex]\frac{117.3\ feet}{second} = \frac{0.022216\ (Approx)}{0.00028\ (Approx)}[/tex]
117.3 feet per second = 79.8 miles per hours (Approx)
Thus
[tex]v_{source}= 79.8\ miles\ per\ hours[/tex]
Therefore the 79.8 miles per hours fast is the car going.
