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You are at a stop light in your car, stuck behind a red light. Just before the light is supposed to change, a fire engine comes zooming up towards you traveling at a horrendous 85.0 km/h. If the siren has a rated frequency 665 Hz, what frequency of the sound do you hear

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Answer:

The frequency of the sound you will hear is 713.85 Hz

Explanation:

Given;

speed of your car, [tex]v_s[/tex] = 85.0 km/h

frequency of the siren, f = 665 Hz

Speed of sound in air, v = 345 m/s

The frequency of the sound you hear, can be calculated as;

[tex]f' = f(\frac{v}{v-v_s})[/tex]

Convert the speed of the car to m/s

[tex]85 \ km/h =\frac{85 \ km}{h} (\frac{1000\ m}{1 \ km})(\frac{1 \ h}{3600 \ s} ) = 23.61 \ m/s[/tex]

[tex]f' = f(\frac{v}{v-v_s} )\\\\f' = 665(\frac{345}{345-23.61} )\\\\f' = 665 (1.07346)\\\\f' = 713.85 \ Hz[/tex]

Therefore, the frequency of the sound you will hear is 713.85 Hz

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