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A police car's siren operates at a frequency of 2,000 Hz. What frequency would a stationary listener observe if the police car is driving towards him at 65 mph? Note vsound = fλ, where vsound (the speed of sound in air) is 345 m/s. Also, 1 mile = 1.609 km.

Respuesta :

we can use formula

[tex]f_L=f_s(\frac{v_a-v_p}{v_a+v_p} )[/tex]

where

fL is listener frequency

fs is siren frequency

va is the speed of sound in air

vs is police car speed

so, we have

[tex]f_s=2000Hz[/tex]

[tex]v_a=345m/s[/tex]

[tex]v_p=65mph[/tex]

now, we can change it into m/s

[tex]v_p=65*\frac{1609}{3600}m/s[/tex]

[tex]v_p=29.05139m/s[/tex]

now, we can plug it

[tex]f_L=2000(\frac{345-29.05139}{345+29.05139} )[/tex]

[tex]f_L=1689.33263Hz[/tex]..............Answer

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