A clarinet is an instrument which acts like an \"open-closed\" tube. Suppose you

Question

A clarinet is an instrument which acts like an "open-closed" tube. Suppose you play a note which is the fundamental of the instrument (with all holes closed) which is at 220 Hz. What is the frequency of the next harmonic you can play?

If the second harmonic of a guitar string is at a frequency of 470 Hz, what is the frequency of the fifth harmonic?

A stereo is playing music with an output of 80 dB. If the volume is turned up so that the output intensity is 10000 times greater, what will be the new intensity level?

Explanation / Answer

Part 1)

In that kind of tube, the standing wavelength of the fundamental is 4 times the tube length

Using v = f(wavelength)

343 = 220(wavelength)

wavelength = 1.559, so tube length = .390 m

The next harmonic is when 3/4 of a wave are in the tube.

The .75(wavelength) = .390

wavelength = .520 m

Then v = f(wavelength)

343 = f(.520)

f = 660 Hz

Part 2)

If the second is at 470, the first is half that which is 235

The 5th is five times the first = 235(5) = 1175 Hz

Part 3)

Start with B = 10log I/Io

80 = 10log(I/1 X 10-12)
I = .0001

The new intensity = (.0001)(10000) = 1

The new level is 10 log (1/1 X 10-12)

B = 120 dB

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