One of the harmonic frequencies of tube A with two open ends is 840 Hz. The next

Question

One of the harmonic frequencies of tube A with two open ends is 840 Hz. The next-highest harmonic frequency is 910 Hz. (a) What harmonic frequency is next highest after the harmonic frequency 560 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 4340 Hz. The next-highest harmonic frequency is 4588 Hz. (c) What harmonic frequency is next highest after the harmonic frequency 2356 Hz? (d) What is the number of this next-highest harmonic?

Explanation / Answer

for open ended pipe fn = n*f1 n is integer fn = 1020 Hz, fn+1 = 1088 Hz f1 = fn+1-fn = 68 Hz => n = 15 next harmonic frequency after 952 Hz = 952+68 = 1020 Hz number is 1020/68 = 15 C) for one closed end fn = n*f1 where n is odd fn = 4551 Hz fn+2 = 4797 Hz => 2*f1 = 246 => f1 = 123 Hz next highest after 2337 Hz = 2337+2*123 = 2583 Hz number is 2n+1 = 2583/(123) => n = 10

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