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 100hertz tone." Alicia says
"It's Beto. I'm playing a 440 hertz 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.