Question

Problem 2 Two guitarists Alicia and Beto are maintaining social distance in separate booths in a recording studio, each has a guitar that produces pure sine waves (without harmonics). Alicia can hear Beto's guitar through her headphones and Beto can hear Alicia's guitar through his headphones. Chris, the sound technician, listens to both guitars on his headphones. Alicia and Beto play the same note and Chris complain: "One of you is out of tune, I hear a 100 hertz tone." Alicia says "it's Beto. I'm playing a 440 hertz tone." Beto then tunes his guitar and once again they both play 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 works perfectly, how do you explain that Chris can't hear anything after playing the 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