A train is moving parallel to a highway with a constant speed of 19.5 m/s. A car is traveling in the same direction as the train with a speed of 40.5 m/s. The car horn sounds at a frequency of 512 Hz, and the train whistle sounds at a frequency of 322 Hz. (a) When the car is behind the train, what frequency does an occupant of the car observe for the train whistle? Hz (b) After the car passes and is in front of the train, what frequency does a train passenger observe for the car horn?

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CarliReifsteck CarliReifsteck · Answer 1 · 2019-08-22T13:36:45+02:00

Answer:

(a). The frequency of the car is 990.76 Hz.

(b). The frequency of the train is 265.48 Hz.

Explanation:

Given that,

Speed of train = 19.5 m/s

Speed of car = 40.5 m/s

Frequency of car's horn = 512 Hz

Frequency of train's whistle = 322 Hz

(a). When the car is behind the train,

We need to calculate the frequency of the car

Using formula of frequency

[tex]f_{c}=f_{t}(1+\dfrac{v_{c}}{v_{t}})[/tex]

Put the value into the formula

[tex]f_{c}=322\times(1+\dfrac{40.5}{19.5})[/tex]

[tex]f_{c}=990.76\ Hz[/tex]

(b). After the car passes and is in front of the train,

We need to calculate the frequency of train

Using formula of frequency

[tex]f_{t}=f_{c}(1+\dfrac{v_{c}}{v_{t}})[/tex]

Put the value into the formula

[tex]f_{t}=512\times(1-\dfrac{19.5}{40.5})[/tex]

[tex]f_{c}=265.48\ Hz[/tex]

Hence, (a). The frequency of the car is 990.76 Hz.

(b). The frequency of the train is 265.48 Hz.