The amplitude of a standing sound wave in a long pipe closed at the left end is

Question

The amplitude of a standing sound wave in a long pipe closed at the left end is sketched below.

1.The vertical axis is the maximum displacement of the air, and the horizontal axis is along the length of the pipe. What is the harmonic number for the mode of oscillation illustrated?

2.The length of the pipe is 0.350 m. What is the pitch (frequency) of the sound? Use 340 m/s for the speed of sound in air.

3.The pipe is now held vertically, and a small amount of water is poured inside the pipe. The first harmonic frequency is then measured to be 296.3 Hz. Measuring from the bottom of the pipe, what is the level of the water?

Explanation / Answer

1) Third harmonic

2) given v = 340 m/s
L = 0.35 m
f = ?

f3 = 3*v/(4*L)

= 3*340/(4*0.35)

= 729 Hz

3) let L' is the new length of the air column.

f1 = v/(4*L')

L' = v/(4*f1)

= 340/(4*296.3)

= 0.287 m

height of water column = L - L'

= 0.35 - 0.287

= 0.063 m or 6.3 cm

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