# Need help on physics problem?

When the slide of a trombone is extended, the length of the column of vibrating air increases. Since the speed of sound does not vary, we observe that the frequency of the note being played...

(Don't know whether it increases, decreases, or stays the same.)

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• velocity = frequency x wavelength

"Since the speed of sound does not vary," increasing the wavelength must DECREASE the frequency.

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• The wave (or at least half of it) must fit into the length of the tube.  If the length is longer then it takes more time to go up the tube and back so it makes fewer cycles in each second.  ie the frequency must be lower.  There are other modes where we fit MORE than one wave into the tube.

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• If the length of the string is L, the fundamental harmonic is the one produced by the vibration whose nodes are the two ends of the string, so L is half of the wavelength of the fundamental harmonic. Hence one obtains Mersenne's laws:

(Frequency) f = 1/2L√[T/µ]

where T is the tension (in Newtons), µ is the linear density (that is, the mass per unit length), and L is the length of the vibrating part of the string.

=>f is inversely proportional to L

=>if L increases, f decreases

=>if L decreases, f increases

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• Longer = lower frequency.  Just like with a guitar string.

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