Please answer each part of the following question: The amplitude of a standing s

Question

Please answer each part of the following question:

The amplitude of a standing sound wave in a long pipe closed at the left end and open at the right end is sketched below. 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? The length of the pipe is 0.410 m. What is the pitch (frequency) of the sound? Assume that the speed of sound is 310 m/s. 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 230.6 Hz. Measuring from the bottom of the pipe, what is the level of the water?

Explanation / Answer

(1)

Of an open ended pipe, odd harmonics are allowed (3rd overtone)

Thus, the harmoic number : 7th Harmonic

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(2)

Equation for the frequency of nth harmonic:

f = n v / 4 L

In this case, n = 7, thereore

f = 7 ( 310 ) / 4 ( 0.41) = 1323.1Hz

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(3)

Let level of water H, If reduces the effective length of pipe

Use the frequency equation,

f = n v / 4 Leff

Here, n = 1

230.6 = 1 x 310 / 4 ( 0.41 - H)

Solve the equation for H

H = 0.0739m

H = 7.39 cm

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