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. The vertical axis is the maximum displacement of the air, and the horizontal axis is along the lenqth of the pipe. What is the harmonic number for the mode of oscillation illustrated? Submit Answer Tries 0/12 The length of the pipe is 0.320 m. What is the pitch (frequency) of the sound? Use 340 m/s for the speed of sound in air. Submit Answer Tries 0/12 The pipe is now held vertically, and a small amount of water is poured inside the pipe. The first harmonic freguency is then measured to be 324.1 Hz. Measuring from the bottom of the pipe, what is the level of the water?

Explanation / Answer

a) 7th harmonic

b) L = 0.32 m
v = 340 m/s

f_7 = 7*v/(4*L)

= 7*340/(4*0.32)

= 1859 Hz

c)

letL' is the length of the air column

f1 = v/(4*L')

L' = v/(4*f)

= 340/(4*324.1)

= 0.2623 m

level of water = L - L'

= 0.320 - 0.262

= 0.058 m or 5.8 cm

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