Angular velocity, the Doppler effect, and frequencies.

[sirfinklstin]

Homework Statement

A speaker is attached to a wire 1.5 m long and is spun in a circle at 2 rev/s. The speaker is connected to an electric piano on which a child is playing a note at 261 Hz. Speed of sound in air is 343 m/s.

What range of frequencies will the stationary observer hear?

I converted rev/s to rad/s to get angular velocity, w=720.0027707 rad/s.
Then, I converted this into linear velocity to match with the speed of sound, v/r = w, v = 1080.004156 m/s.

Next I used the Doppler equation for a moving source, and got 198.0887291 and 382.4685762Hz, is this correct?

 

[nasu]

You can see that the linear speed of the speaker is larger than the speed of sound... no second thoughts?

The angular velocity is 4pi rad/s (1 rev=2pi, 2rev=4pi) or approx 12.56 rad/s.
I don't undersdtand how you can get that number (w=720.0027707 rad/s.) unless you used degrees and and a slide ruler to multiply 2 by 360.

 

[sirfinklstin]

after using your 12.56 rad/s, i got 8.3733 m/s and 6.2197 to 6.5309Hz as my range of frequencies, but this does not seem right. Am I missing something?

 

[nasu]

The linear velocity is given by
v=w*r where w is the angular velocity and r is 1.5 m.
How do you get 8.4 if w is about 12.6 and r=1.5?? It is about 19 m/s .(the 4 digits after the decimal point are pointless).

The range of frequencies should be something around the basic frequency (261 Hz).
Like 255-266 Hz (as an example, I did not do the calculation).
You need to calculate the frequency increase when the source approaches the observer and the decrease when the source is going the other way.

 

[sirfinklstin]

The range of velocities are 247 to 276 Hz. I divided the angular velocity by the radius instead of multiplying it (thanks for pointing that out). Also I had the variable for Vsound and V source mixed up! Thanks for the help!