One of the harmonic frequencies of tube A with two open ends is 1224 Hz. The nex

Question

One of the harmonic frequencies of tube A with two open ends is 1224 Hz. The next-highest harmonic frequency is 1292 Hz.(a) What harmonic frequency is next highest after the harmonic frequency 816 Hz? (b) What is the number of this next-highest harmonic? One of the harmonic frequencies of tube B with only one open end is 2356 Hz. The next-highest harmonic frequency is 2604 Hz.(c) What harmonic frequency is next highest after the harmonic frequency 620 Hz? (d) What is the number of this next-highest harmonic? Number Units Number Units Number Units Number Units

Explanation / Answer

The frequency will have an anti-node at both open ends.
First harmonic frequency:
1292 Hz - 1224 Hz = 68 Hz

a) 816 Hz + 1st harmonic(68 Hz) = Next harmonic (884 Hz) (Answer)
b) Harmonic frequency / 1st harmonic frequency = Harmonic number
884/68 = 13 (Answer)
c) For the tube with one closed end:
- only odd harmonic frequencies are possible (where the harmonic number is 1, 3, 5, 7,9, ...)
- there is a node at the closed end and an anti-node at the open end.

So the two harmonic frequencies that are given are actually 2 harmonic frequencies apart, since even number harmonic frequencies are not possible in a tube with one open end.

So therefore, (one harmonic frequency - the harmonic frequency before it)/2 = the 1st harmonic frequency.

First harmonic frequency = (2604 - 2356)/2 = 124 Hz

We require to add the first harmonic frequency twice in order to skip the even harmonic frequency

So, 620 Hz + (2* 124) = 868 Hz (Answer)
d) 868 / 124 = 7 (Answer)

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