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## Homework Statement

Two trains emit 516-Hz whistles. One train is stationary. The conductor on the stationary train hears a 3.5-Hz beat frequency when the other train approaches. What is the speed of the moving train?

b = beat

f'_b = 3.5 Hz

f = 516 Hz

## Homework Equations

f_b = |f_1 - f_2|

v_sound = 343 m/s (speed of sound in 20°C air)

Doppler equation for "source moving toward stationary observer":

f' = f/(1+(v_source/v_sound))

## The Attempt at a Solution

First I'll tweak the beat frequency equation to solve for what the stationary train conductor hears as the frequency of the moving train's whistle.

f'_b = |f' - f| <<< f' > f since the train is moving TOWARD him.

3.5 Hz = |f' - 516 Hz|

f' = 519.5 Hz

Now I'll substitute all values into the Doppler equation to find the velocity of the moving train.

519.5 Hz = 516 Hz / (1 - (v_source / 343 m/s) )

v_source = 2.31 m/s

Though possible, this seems like a low speed for a moving train. Did I do everything correctly?

Thank you!