Solving for the RPM of a Malfunctioning Motor

[akan]

Homework Statement

Suppose you're operating a machine with two motors. If the two motors are not operating at the same rpm, you will hear a periodic variation in the intensity of the sound-that is, beats. Suppose the tachometer that indicates the rotation rate of one motor is malfunctioning. The operational one shows 3600 rpm. You hear a beat every 21 s. You are certain the other motor is running fast.

What is its rotational speed in rpm?

Homework Equations

w1-w2 is the frequency of amplitude change (according to the textbook).

3. Attempt at solution
delta_w = 2pi/T = w1-w2
w1 - 2pi/T = w2

w2 is not valid (given that I have converted all units to standard and back into rpm). So I think my formula isn't valid. Can someone derive a correct one please? Thanks.

 

[LowlyPion]

Homework Statement

Suppose you're operating a machine with two motors. If the two motors are not operating at the same rpm, you will hear a periodic variation in the intensity of the sound-that is, beats. Suppose the tachometer that indicates the rotation rate of one motor is malfunctioning. The operational one shows 3600 rpm. You hear a beat every 21 s. You are certain the other motor is running fast.

What is its rotational speed in rpm?

Homework Equations

w1-w2 is the frequency of amplitude change (according to the textbook).

3. Attempt at solution
delta_w = 2pi/T = w1-w2
w1 - 2pi/T = w2

w2 is not valid (given that I have converted all units to standard and back into rpm). So I think my formula isn't valid. Can someone derive a correct one please? Thanks.

How many times has one motor turned in 21 seconds?

If during the beat the "faster" one precessed such that you discrened a "beat" wouldn't that mean that the faster one - over that time - rotated 1 more complete time than the other?

 

[akan]

>> How many times has one motor turned in 21 seconds?
The first one rotated 3600 rpm * m/60s * 21s times. I don't know about the second one since it's the one I need to find.

>> If during the beat the "faster" one precessed such that you discerned a "beat" wouldn't that mean that the faster one - over that time - rotated 1 more complete time than the other?

Why would it be "1" more complete time than the other? How do I know how many more times it rotated? How is this tied into the formula? Thanks.