Consider a situation where a source is emitting a painfully high frequency sound and you want to reduce the observed frequency of the sound by a proportion p, where 0 < p < 1.ª a. With what speed (as a function of the speed of sound, v) must the source must move away from a stationary observer for the observer to hear the sound with the desired reduced frequency?
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
My answer is incorrect, please write your explanation(process detail) why the answer is v(p)/(1-p) and write why my answer is wrong.
I attach the image and write my process of explanation.
My solution:
When the source is moving away with a speed of vs.
Using Doppler's effect for this case,
f=fo(v/v+vs)
Then the speed f source will be
vs=(fo/f)-1v
putting the values
vs=(fo/pfo)-1v=1p-1v
Hence, the speed of the source (moving away) is vs=1p-1v.
Professor's solution and answer I attach in the image.
Given:
Frequency emitted by source = f
New expected frequency is p times f where p is between 0 and 1.
Stationary observer
Speed of source = v
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