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

Question

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?

in progress 0
Farah 4 years 2021-08-29T13:56:30+00:00 1 Answers 108 views 0

Answers ( )

  1. Edana
    0
    2021-08-29T13:58:12+00:00
    Reply

    Answer:

    (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

    f_{obs} = \dfrac{vf_{source}}{v-v_{source}}

    350Hz = \dfrac{343f_{source}}{343-v_{source}}

    solving for f_{source} we get:

    f_{source} = \dfrac{350(343-v_{source})}{343}.

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

    340Hz = \dfrac{343f_{source}}{343-\dfrac{v_{source}}{2} }

    substituting the value of f_{source} we get:

    340Hz = \dfrac{343\dfrac{350(343-v_{source})}{343}}{343-\dfrac{v_{source}}{2} }

    340Hz = \dfrac{350(343-v_{source})}{343-\dfrac{v_{source}}{2} }

    340Hz = \dfrac{700(343-v_{source})}{686-v_{source}}

    340 (686-v_{source}) = 700(343-v_{source})

    \boxed{v_{source} = 19.0m/s}

    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,

    v_{after} = \dfrac{v_{source}}{2}

    \boxed{v_{after} =9.5m/s}

    or 34.3 km per hour.

Leave an answer

Browse

Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )