Final answer:
To find the velocity of the emergency vehicle, apply the Doppler Effect formula and substitute the given frequencies and the speed of sound at the given temperature. This will yield the vehicle's velocity relative to the stationary listener.
Step-by-step explanation:
The subject question involves solving for the velocity of an emergency vehicle using the observed frequencies and the known frequency emitted by the siren, a concept that is explained by the Doppler Effect. The Doppler Effect describes how the frequency of a wave (in this case, sound) changes from the perspective of a stationary observer as the source of the wave moves relative to them.
We can calculate the speed of the vehicle using the formula derived from the Doppler Effect for sound,
f' = f(v + vo) / (v + vs),
where f' is the observed frequency (490 Hz), f is the emitted frequency (440 Hz), v is the speed of sound in air, vo is the observer's velocity (0 m/s since the observer is stationary), and vs is the source's velocity which is what we are trying to find. The speed of sound in air at 20 °C is typically 343 m/s.
Rearranging the equation to solve for vs, we get
vs = v(f' / f - 1)
Plugging in the values, we find
vs = 343 m/s * (490 Hz / 440 Hz - 1)