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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 206 Hz, and the other trucker hears a frequency of 189 Hz, determine the speed of the trucks. Use the speed of sound as 343 m/s. m/s

Respuesta :

Answer:

v' = 14.76 m/s

Explanation:

given,

frequency of the one truck = 206 Hz

apparent frequency ,f' = 189 Hz

speed of sound, v = 343 m/s

speed of observer (v_o)and source (v_s) = v'

now, using Doppler's effect

[tex]f' = \dfrac{v-v_o}{v+v_s}\ f[/tex]

[tex]f' = \dfrac{v- v'}{v+v'}\ f[/tex]

[tex]189 = \dfrac{343- v'}{343+v'}\ 206[/tex]

[tex]0.9174= \dfrac{343- v'}{343+v'}[/tex]

314.69 + 0.9174 v' = 343 - v'

1.9174 v' = 28.30

v' = 14.76 m/s

hence, the speed of the truck is equal to 14.76 m/s

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