Doppler Effect in Circular Motion

[confusedinphys]

[SOLVED] Doppler Effect in Circular Motion

Homework Statement

A Physics professor annoys his students by tying a 500 Hz generator to a 60cm long string and whirling it around his head at 100 rpm. What are the highest and lowest frequencies heard by the students?

Homework Equations

The Attempt at a Solution

 

[learningphysics]

What is the equation for doppler effect?

What is the speed of the generator when the professor is twirling it? suppose the students are gathered at together right in front of the professor...

In the circular path of the generator when is the generator moving fastest towards the students... this gives the maximum frequency... when does it move fastest away from the students... this gives the minimum frequency.

 

[ogb p]

The highest frequency heard by the students will be when the generator is moving towards them at the fastest rate, which is when the string is perpendicular to the line connecting the generator to the students. This will occur when the string is at the top of the circle. The frequency in this case will be given by the formula f = f0 (v+v0)/(v-vS), where f0 is the original frequency (500 Hz), v is the speed of sound (assumed to be 343 m/s), v0 is the speed of the generator (100 rpm = 10.47 rad/s), and vS is the speed of the string (which is equal to v0). Plugging in these values, we get a frequency of approximately 537 Hz.

The lowest frequency heard by the students will be when the generator is moving away from them at the fastest rate, which is when the string is parallel to the line connecting the generator to the students. This will occur when the string is at the bottom of the circle. Using the same formula as before, we get a frequency of approximately 463 Hz.

The Doppler effect in circular motion can be observed when an object is moving in a circular path and the observer is not in the same plane as the object's motion. This results in a change in frequency due to the relative motion between the source and the observer. In this case, the generator is the source and the students are the observers. As the generator moves towards the students, the frequency increases due to the compression of sound waves, and as it moves away from the students, the frequency decreases due to the expansion of sound waves. This phenomenon is commonly observed in everyday life, such as when a siren of a passing ambulance or police car sounds higher as it approaches and lower as it moves away. In the case of circular motion, the frequency change is dependent on the speed of the source and the speed of sound, as well as the angle between the source and the observer.