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Two train whistles have identical frequencies of 180 Hz. When one train is at rest in the station, sounding its whistle, a beat frequency of 3.7 Hz is heard from a train moving toward us. Find the speed of the train. (Take the speed of sound to be 345 m/s.)

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lublana

Answer:

7 m/s

Step-by-step explanation:

We are given that

Frequency at stationary =[tex]f_0=180Hz[/tex]

Beat frequency=3.7 Hz

Apparent frequency=[tex]f=180+3.7=183.7Hz[/tex]

Speed of sound=v=345 m/s

We have to find the speed of train

Apparent frequency=[tex]f=f_0(\frac{v}{v-v_s})[/tex]

Substitute the values then we get

[tex]183.7=180(\frac{345}{345-v_s})[/tex]

[tex]345-v_s=\frac{180\times 345}{183.7}[/tex]

[tex]345-v_s=338[/tex]

[tex]v_s=345-338=7 m/s[/tex]

Hence, the speed of train=7 m/s

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