# Working out the speed of a object by its frequency and a superposition wave?

Say you have 2 loudspeakers facing each other and they are separated by 20m, but are connected to the same oscillator and so both have a signal frequency of 800Hz. I calculated the separation of the nodes to be 0.213m because $\lambda = \frac{v}{f}$, and the speed of sound is 340m/s, so the separation of the nodes is the wavelength divided by 4 (anti-node to node).

But then say then there was a microphone travelling at a constant speed from one end to the other and it records a signal that varies periodically at 5Hz. How would you calculate the speed at which the microphone is moving?

To me that reads as "every second it gains 5Hz in the signal". But I'm just not sure because I'm not sure if thats what it means by periodically.

• It means they pass through an anti-node five times a second. – M. Enns Apr 4 '16 at 19:45

Due to the Doppler effect, the microphone receives two signals, one at $f_1>800~$Hz from one speaker and one at $f_2<800~$Hz from the other.
The superposition of both results in a beat. Here, a 800 Hz sine modulated by a sine of frequency $(f_1-f_2)/2$ (the frequency of the amplitude modulation is $f_1-f_2$, because the amplitude is the absolute value of the latter sine).