A train whistle is heard at 350 Hz as the train approaches town. The train cuts its speed in half as it nears the station, and the sound of the whistle is then 340 Hz.

a. What is the speed of the train before slowing down?
b. What is the speed of the train after slowing down?

Given:

Train whistle,

Sound of whistle,

Speed of sound,

Now,

→ ...(equation 1)

→ ...(equation 2)

After dividing "equation 1" by "equation 2", we get

→

By applying cross-multiplication, we get

→

→

                                        (Speed before train slowing down)

hence,

Speed after train slowing down will be:

=

=

=

Thus the responses above are correct.

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(a). 19.0 m/s

(b). 9.5m/s

Explanation:

Assuming speed of sound is 343m/s.

(a).

As the train approaches, from the the Doppler equation we have

solving for we get:

.

And as the train cuts its speed in half, the equation gives

substituting the value of we get:

or 68.6 km per hour, which is the speed of the train before slowing down.

(b).

The speed of the train after slowing down is half the previous speed; therefore,

or 34.3 km per hour.