Question

Two guitar players Alicia and Beto are keeping social distancing in separate booths in a recording studio, each one has a guitar that produces pure sound waves (no harmonics). Alicia can hear Beto’s guitar through her earphones and Beto can hear Alicia’s guitar through his. Chris, the sound technician, hears both guitars on his earphones. Alicia and Beto strike the same note and Chris complains “One of you is out of tune I hear a 100 hertz tone.” Alicia says “It’s Beto. I’m playing a 440 hetz tone”. Beto then tunes his guitar and one more time, both strike the same 440 hertz note. This time Chris complains “I don’t hear anything”.

Part a

What are the possible frequencies of Beto’s guitar note before he tuned his guitar? Show your calculations.

Part b

All the electronic equipment in the recording studio is working perfectly, how do you explain that Chris can’t hear anything after beto tunes his guitar? Include a diagram of the two notes (sine waves) to support your explanation.

Part c

If instead of pure sine waves the guitar included up to the fifth harmonic, what would be the frequencies of the second and third harmonics for the 440 hertz note. Include your calculations

Answer 1