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Two truckers are traveling directly away from each other at the same speed. If one trucker sounds her horn at a frequency of 211 Hz, and the other trucker hears a frequency of 187 Hz, determine the speed of the trucks. Use the speed of sound as 343 m/s.

Respuesta :

Answer:

The speed of the truck is 20.68 m/s.

Explanation:

Given that,

Frequency of horn = 211 Hz

Trucker hears a frequency = 187 Hz

Speed of sound = 343 m/s

Let the speed of the truck is [tex]v_{T}[/tex]

We need to calculate the speed of truck

Using Doppler shift

[tex]f = f_{0}\dfrac{v'-v_{0}}{v'+v_{s}}[/tex]

Where, [tex]f_{0}[/tex] = horn frequency

f = Trucker hears a frequency

v'=speed of sound

[tex]v_{0}[/tex] = speed of observer

v = speed of source

Put the value in to the formula

[tex]187=211\times(\dfrac{343+v_{T}}{343+v_{T}})[/tex]

[tex]v_{T}=\dfrac{211\times343-187\times343}{398}[/tex]

[tex]v_{T}=20.68\ m/s[/tex]

Hence, The speed of the truck is 20.68 m/s.

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