Question

you are standing on the sidewalk as a firetruck drives toward you at 13 m/s. the siren on the truck is emitting sound waves, which you perceive to be at a frequency of 400 hz. what is the actual frequency being emitted by the siren (in hz)?

Answer 1

The actual frequency of the siren emitting sound waves perceived at 400 Hz as a firetruck approaches at 13 m/s can be calculated using the Doppler Effect formula, which is approximately 385 Hz.

Step-by-step explanation:

The question asks for the actual frequency of the siren from a firetruck when you perceive the frequency as 400 Hz while the truck is moving toward you at 13 m/s. This effect is known as the Doppler Effect, which describes the change in frequency of a wave in relation to an observer moving relative to the source of the wave. To solve this, we can use the Doppler Effect formula for a source moving towards a stationary observer: f' = f (v + v_o) / (v - v_s), where f' is the observed frequency, f is the actual frequency to find, v is the speed of sound in air (typically around 343 m/s at room temperature), v_o is the velocity of the observer (which is 0 since the observer is stationary), and v_s is the velocity of the source.

Rearranging the equation to solve for f gives:

f = f' (v - v_s) / v

Substituting the given values:

f = 400 Hz (343 m/s - 13 m/s) / 343 m/s

f ≈ 400 Hz * 330 / 343

f ≈ 385 Hz

So, the actual frequency of the siren is approximately 385 Hz.