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A car approaches you at a constant speed, sounding its horn, and you hear a frequency of 76 Hz. After the car goes by, you hear a frequency of 65 Hz. What is the frequency of the sound emitted by the horn

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opudodennis

Answer:

70.07 Hz

Explanation:

Since the sound is moving away from the observer then

[tex]f_o = f_s\frac {(v+vs)}{v}[/tex] and [tex]f_o = f_s\frac {(v-vs)}{v}[/tex] when moving towards observer

With [tex]f_o[/tex] of 76 then taking speed in air as 343 m/s we have

[tex]76 = f_s\times\frac {(343-vs)}{343}[/tex]

[tex]f_s=\frac {343\times 76}{343-v_s}[/tex]

Similarly, with [tex]f_o[/tex] of 65 we have

[tex]65 = f_s\times\frac {(343+vs)}{343}\\f_s=\frac {343\times 65}{343+v_s}[/tex]

Now

[tex]f_s=\frac {343\times 65}{343+v_s}=\frac {343\times 76}{343-v_s}[/tex]

v_s=27.76 m/s

Substituting the above into  any of the first two equations then we obtain

[tex]f_s=70.07 Hz[/tex]

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