Doppler Effect frequencies Question

[almeidamyers]

Homework Statement

An object producing a sound with frequency 500 Hz is traveling at 40 m/s toward an observer, and the observer is traveling at 30 m/s away from the source. Another source producing a sound with the same frequency is traveling at 10 m/s toward a stationary observer. Determine the frequencies perceived by each of the observers, assuming that the speed of sound in air is 345 m/s. Are the two frequencies the same? If not, what causes the difference between the perceived frequencies?

Homework Equations

f' = f*(v+v_o)/(v-v_s)

v = speed of sound = 345 m/s
v_o = speed of observer toward source
v_s = speed of source toward observer

The Attempt at a Solution

I've figured out that the frequency perceived by the first observer (traveling at 30 m/s) is 516 Hz, while the frequency perceived by the second observer (stationary) is 514.9 Hz.


I understand mathematically why this happens. What I can't figure out is what physically occurs that would make the frequencies perceived by the two observers differ when the relative velocities between the observer and the source are the same in both cases.

Thanks in advance for any help you can give me.

 

[rl.bhat]

Frequency of the source always remains constant. Due to the motion of the source apparent wave length changes. If the observer is stationary, the same apparent wavelength is received by him. Mathematically f'/v = f/(v - vs). If the observer also in motion,the apparent wave length further changes. Mathematically f'/(v-vo) = f/(v - vs).
In all these expression, the relative velocity between sound and source or sound and observer is considered, not the source and observer..

 

[nlightner]

The difference in perceived frequencies between the two observers is due to the Doppler Effect. This is a phenomenon in which the frequency of a wave (in this case, sound) appears to change when the source of the wave and the observer are in motion relative to each other.

In the first scenario, the observer is moving towards the source, causing the perceived frequency to increase. This is because as the observer moves closer to the source, the sound waves are compressed, resulting in a shorter wavelength and a higher frequency. Conversely, in the second scenario, the observer is stationary while the source is moving towards them. This causes the perceived frequency to decrease because the sound waves are stretched out as they travel towards the stationary observer, resulting in a longer wavelength and a lower frequency.

The difference in perceived frequencies between the two observers is also affected by the speed of sound in air. In this case, the speed of sound is constant at 345 m/s, but if it were to change, it would also impact the perceived frequencies.

In summary, the perceived frequencies differ due to the relative motion between the observer and the source, as well as the speed of sound in the medium. This is a well-documented phenomenon known as the Doppler Effect, and it is used in many fields of science, including astronomy and meteorology, to study the motion and properties of objects in space and in our atmosphere.