Question

One day when the speed of sound in air is 343 m/s, a fire truck traveling at vs = 29 m/s has a siren which produces a frequency of fs = 401 hz. vs = 29 m/s f = 401 hz what frequency, in units of hertz, does an observer hear when the truck is moving away?

Answer 1

Using the Doppler Effect formula, the observed frequency of the siren from a fire truck moving away at 29 m/s, when the speed of sound is 343 m/s, is approximately 385 Hz.

Step-by-step explanation:

The question at hand involves the Doppler Effect, which describes the change in frequency of a wave with an observer moving relative to the source of the wave. In this context, the observer is hearing the sound of a siren from a fire truck moving away from them.

Calculation of Observed Frequency

The formula for the Doppler Effect for a source moving away from a stationary observer is given by:

f' = f * (v / (v + vs))

Where:

• f' is the observed frequency

• f is the source frequency (401 Hz)

• v is the speed of sound in air (343 m/s)

• vs is the speed of the source (29 m/s)

Substituting the given values, we get:

f' = 401 * (343 / (343 + 29))

Calculating this gives us the observed frequency when the truck is moving away:

f' ≈ 385 Hz