The following figures depict cross sections of open pipe (a) and stopped pipe (b

Question

The following figures depict cross sections of open pipe (a) and stopped pipe (b) showing the three modes for resonance of sound, respectively. (Note: From top to bottom, in open pipe(a), we call the frequencies fundamental frequency, second harmonic frequency and third harmonic frequency, respectively. In stopped pipe (b), we call the frequencies fundamental frequency, third harmonic frequency and fifth harmonic frequency, respectively.) a) b) Match the corresponding frequency (fi) to each standing-wave pattern. (Note: v is the speed of sound, and Lcorr is negligible.) fundamental frequency (f1) for a) Choose [Choose ] V/4L 5v/4L 3v/4L 3v/2L V/2L v/L second harmonic frequency (f2) for a) third harmonic frequency (f3) for a) fundamental freqency (f1) for b) Choose ] third hamonic freqency (f3) for b) Choose ] fifth hamonic freqency (f5) for b) Choose

Explanation / Answer

1)

f1 for a)

here lambda/2 = L

lambda = 2 L

use:

f = speed/lambda

= V/2L

Answer: V/2L

2)

f2 for a:

lambda = L

f = speed/lambda

= V/L

Answer: V/L

3)

f2 for a:

3lambda/2 = L

lambda = 2L/3

USE:

f = speed/lambda

= 3V/2L

Answer: 3V/2L

4)

f1 for b)

Here lambda/4 = L

lambda = 4L

use:

f = speed/lambda

= V/4L

Answer: V/4L

5)

f3 for b:

Here lambda/2 + lambda/4 = L

3lambda/4 = L

lambda = 4L/3

f = speed/lambda

= 3V/4L

Answer: 3V/4L

6)

f5 for b:

Here lambda + lambda/4 = L

5lambda/4 = L

lambda = 4L/5

f = speed/lambda

= 5V/4L

Answer: 5V/4L

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