3B60.10 Beat forks

Two tuning forks differing by a variable amount are mounted on resonance boxes. Students in back of large rooms may not be able to hear beat note. The output can be fed to a microphone connected to scope to provide visual display.

Setup Requirements: Off the Shelf for boxes. Need advance notice to set up and adjust oscilloscope version.

Equations: Amplitude of sound varies in a way that depends on frequency difference.

Safety Issues: AC voltage present

Added Information: There are 3 ways of dealing with beat notes beat notes. One is to explain in terms of adding waves. This is best done using transparencies of graphs in text books. The second way is to set up scope display so amplitude of scope pattern varies in the same way as the audible signal. The third and more difficult way is to adjust scope controls for pattern that looks like AM radio modulation. You see one or a half wavelength of pattern due to beat note. "Inside" this low frequency envelope you see the higher frequency oscillations around 1 KHz.

There is some confusion as to whether beat frequency = f(2)-f(1) or beat frequency =(f(2) - f(1)) / 2. Initially the frequency of the overall function may seem to be (f₁-f₂)/2 as this is the frequency of the cosine part. However, because the sin part of the function alternates between negative and positive values many times during one period of the cosine part, it's effect is to create maxima from both the negative and positive regions of the cosine part, making the overall frequency double the cosine's frequency (cos=+vem, sin=+ve then overall = +ve maximum, and cos= -ve, sin=-ve then overall = +ve maximum). This overall frequency is thus the difference of the two starting frequencies (f₁-f₂).