A boy on a bicycle approaches a brick wall as he sounds his horn at a frequency 400 hz. the sound he hears reflected back from t

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5 days ago

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A boy on a bicycle approaches a brick wall as he sounds his horn at a frequency 400 hz. the sound he hears reflected back from t

he wall is at a frequency 408 hz. at what is the speed is the boy riding his bicycle toward the wall? assume the speed of sound in air is 340 m/s.

Physics

1 answer:

Softa [913] · Answer 1 · 2026-02-28T08:51:38+03:00

The question pertains to the change in frequency of a wave noted by an observer moving in relation to the source, indicating that the concept to invoke is "Doppler's effect."

The standard formula for the Doppler effect is:
$f = (\frac{g + v_{r}}{g + v_{s}})f_{o}$ -- (A)

Note that we don’t need to be concerned with the signs here, as all entities are moving toward each other. If something was moving away, a negative sign would apply, but that is not relevant to this scenario.

Where,
g = Speed of sound = 340m/s.
$v_{r}$ = Velocity of the observer relative to the medium =?.
$v_{s}$ = Velocity of the source in relation to the medium = 0 m/s.
$f_{o}$ = Frequency emitted from the source = 400 Hz.
$f$ = Frequency recognized by the observer = 408 Hz.

Substituting the given values into equation (A) will yield:

$408 = ( \frac{340 + v_{r}}{340 + 0})*400$

$\frac{408}{400} = \frac{340 + v_{r}}{340}$

Solving the above will result in,
$v_{r}$ = 6.8 m/s

The correct result = 6.8m/s