You are wearing earbuds or headphones to listen to your music but your family members can hear it as well. They tell you that it
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Answer:
The speed of the train before and after slowing down is 22.12 m/s and 11.06 m/s, respectively.
Explanation:
We can calculate the speed of the train using the Doppler equation:
Where:
f₀: is the emitted frequency
f: is the frequency heard by the observer
v: is the speed of the sound = 343 m/s
: is the speed of the observer = 0 (it is heard in the town)
: is the speed of the source =?
The frequency of the train before slowing down is given by:
(1)
Now, the frequency of the train after slowing down is:
(2)
Dividing equation (1) by (2) we have:
(3)
Also, we know that the speed of the train when it is slowing down is half the initial speed so:
(4)
Now, by entering equation (4) into (3) we have:
By solving the above equation for we can find the speed of the train after slowing down:
Finally, the speed of the train before slowing down is:
Therefore, the speed of the train before and after slowing down is 22.12 m/s and 11.06 m/s, respectively.
I hope it helps you!