Question

An automobile is traveling away from Jill and towards Jack. The horn is honking, producing a sound wave.

a. Towards which person do the sound waves travel the fastest?
b. Who will hear the highest frequency? Why?

Answer 1

a. The sound will travel at the speed to both Jill and Jack

b. Jack

Step-by-step explanation:

a. Doppler effect describes how the frequency of a sound wave changes with regards to an observer that has relative motion to the sound source;

The Doppler effect is given by the following formula;

For a sound that is moving away, as observed by Jill, we have;

`f' = ((v - v_0))/((v + v_s)) \cdot f = (v )/((v + v_s)) \cdot f`

For approaching sound, as observed by Jack, we have;

`f' = ((v + v_0))/((v - v_s)) \cdot f = (v )/((v - v_s)) \cdot f`

Where;

f = The sound wave's actual frequency

f' = The frequency of the moving sound to the observer

v = The speed of the sound wave

v₀ = The observer's velocity = 0

`v_s` = The velocity of the source (the automobile honking) of the sound wave

From the above equation, we have that the speed of sound, 'v', is the same to both the source, and the observer although the frequency, and therefore, the wavelength of the sound alternatively increases or decreases

b. From the Doppler effect equation, the person who will hear the highest frequency is given by the formula for the frequency when the sound is approaching the observer, which has the lower denominator

Therefore, given that the automobile is travelling towards Jack, jack will hear the higher frequency