The second harmonic sinusoidal standing wave in a pipe with both ends open has a

Question

The second harmonic sinusoidal standing wave in a pipe with both ends open has a wavelength of 2m. The sound speed is 340 m/s.

a) How many nodes and and anti-nodes are there in the displacement wave? How many nodes are there in the pressure wave? Draw the positions of these nodes and anti-nodes.

b) What is the length of the pipe?

c) What is the frequency of the second harmonic?

d) What is the frequency of the fundamental mode in this pipe?

e) If the same pipe was closed at one end and open at the other what would be the frequency of the fundamental mode and the third harmonic?

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Explanation / Answer

Given Second harmonic wave

wavelenth = 2

nodes =2

antinodes = 3

Length of the pipe = 2m

Frequency = V/wavelength =170Hz

wavelenth of the fundamental mode = 1

Fundamental frequency = 340 H

e) for second Harmonic

3/4 *wavelength = L = 2

Wavelength = 8/3

For Fundamental mode

wavelenth = 2/3

Fequency =510Hz

For third Harmonic

Wavelenth = 10/3

Frequency =102 Hz

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