Question

A student knows that an ambulance siren has a frequency of fs = 395 hz. he measures, when the ambulance is approaching him, the frequency fo = 418 hz. assume the speed of sound is 343 m/s in this problem.

Input an expression for the
ambulance's speed, vs, in terms of the
frequencies and the speed of
sound v. vs =

Answer 1

The speed of the ambulance can be found by using the Doppler effect equation, which relates the observed frequency, the source frequency, the speed of sound, and the source's speed. Given the observed frequency of 418 Hz, the source frequency of 395 Hz, and the speed of sound as 343 m/s, the ambulance speed is calculated to be 18.865 m/s.

Step-by-step explanation:

To determine the speed of the ambulance using the Doppler effect equation, we can set up the following relationship:

fo = (fs * v) / (v - vs)

Where fo is the observed frequency, fs is the source frequency, v is the speed of sound, and vs is the speed of the source (ambulance).

We're given fs = 395 Hz, fo = 418 Hz, and v = 343 m/s. Now we can solve for vs:

vs = v * (1 - (fs / fo))

Plugging in our known values:

vs = 343 m/s * (1 - (395 Hz / 418 Hz))

vs = 343 m/s * (1 - 0.945)

Hence:

vs = 343 m/s * 0.055

vs = 18.865 m/s