Question

A train moving toward a station at 10.4 meters per second blows a horn with a frequency of 616 hertz.a. What frequency is heard at the station? Include units in your answer.b. What frequency is heard by a train moving toward the station from the opposite direction at a speed of 20.5 meters per second? Include units in your answer.Suppose instead the first train is moving away from the station at 10.4 meters per second and blows its horn.c. What frequency is heard at the station? Include units in your answer.d. What frequency is heard by a train moving away from the station in the opposite direction at a speed of 20.5 meters per second? Include units in your answer.

Answer 1

ANSWERS

a. 635.26 Hz

b. 673.23 Hz

c. 597.87 Hz

d. 562.14 Hz

Step-by-step explanation

a. In this case, the source is the train moving toward the station. The frequency of the source, fs = 616 Hz, the velocity of the source is vs = 10.4 m/s. The "observer" is the people in the station and we can assume that they are at rest, so the velocity of the observer, vo, is 0 m/s.

We have to find what is the frequency that the observer gets,

`f_o=(v)/(v-v_s)\cdot f_s`

In this formula, v represents the velocity of sound, v = 343 m/s.

The frequency heard by the observer is,

`f_o=(343m/s)/(343m/s-10.4m/s)\cdot616Hz\approx635.26Hz`

Hence, a frequency of 635.26 Hz is heard at the station.

b. This is a different case because the observer is now another train, moving toward the station in the opposite direction - which means that the observer is moving toward the source, and it does it at 20.5 m/s. We also have to find the frequency heard by the observer,

`f_o=(v+v_o)/(v-v_s)\cdot f_s`

Replace with the known values: v = 343 m/s, vo = 20.5 m/s, vs = 10.4 m/s, fs = 616 Hz,

`f_o=(343m/s+20.5m/s)/(343m/s-10.4m/s)\cdot616Hz\approx673.23Hz`

Hence, the other train hears a frequency of 673.23 Hz

c. Now the velocity and frequency of the source are the same, but instead of moving toward the observer, it is moving away from it. The equation changes to,

`f_o=(v)/(v+v_s)\cdot f_s=(343m/s)/(343m/s+10.4m/s)\cdot616Hz\approx597.87Hz`

Hence, the frequency heard at the station will be 597.87 Hz.

d. Again, this case is similar to part b, but in this case, the source and the observer are both moving away from each other, so the equation changes to,

`f_o=(v-v_o)/(v+v_s)\cdot f_s=(343m/s-20.5m/s)/(343+10.4m/s)\cdot616Hz\approx562.14Hz`

Hence, the other train will hear a frequency of 562.14 Hz.