A musical artist fits one piece of PVC (plastic) piping around another to create

Question

A musical artist fits one piece of PVC (plastic) piping around another to create a variable-length tube in which harmonics can be excited by causing the tube to vibrate. She places a microphone on the inside of the tube to record the sound and send it to an amplifier. The tube has a minimum length of 1.3 m and a maximum length of 2.09 m, and the speed of sound in air in the tube is 343 m/s. Suppose she wants to create a sound that has a harmonic frequency of 510.0 Hz. Find each possible length of the tube such that a harmonic frequency of 510.0 Hz is created.

Smallest value=

Middle Value=

Largest Value=

Explanation / Answer

this pipe will act as open ended air column

frequency is given as f=n*v/(2*L)

==>510=n*343/(2*L)

==>n=2.9738*L

minimum value of n=2.9738*1.3=3.86

taking nearest integer value, n=4

maximum value of n=2.9738*2.09=6.2152

so maximum value of n is 6.

then L=n/2.9738

smallest value=4/2.9738=1.3451 m

middle value=5/2.9738=1.6814 m

largest value=6/2.9738=2.0176 m

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