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The amplitude of a standing sound wave in a long pipe closed at the left end is sketched below.
The harmonic number for the mode of oscillation illustrated: 3
The pitch (frequency) of the sound: 580 Hz
Speed of sound in air: 340 m/s
1. 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 251.1 Hz. Measuring from the bottom of the pipe, what is the level of the water?

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onyebuchinnaji

(1) The harmonic number for the mode of oscillation is 3.

(2) The pitch (frequency) of the sound is 580 Hz

(3) The level of the water inside the vertical pipe is approximately 0.1 m.

The harmonic number

The harmonic number for the mode of oscillation illustrated for the closed pipe is 3.

Frequency of the wave

The pitch (frequency) of the sound is calculated from third harmonic formula;

f = 3v/4L

where;

  • v is speed of sound
  • L is length of the pipe

f = (3 x 340) / (4 x 0.44)

f = 579.55 Hz = 580 Hz

level of the water

wave equation for first harmonic of a closed pipe is given as

f  = v/(4L)

251.1  = 340/(4L)

4L = 340/251.1

4L = 1.35

L = 1.35/4

L = 0.34 m

level of water = 0.44 m - 0.34 m = 0.1 m

Thus, the level of the water inside the vertical pipe is 0.1 m.

Learn more about harmonics of closed pipes here: brainly.com/question/27248821

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The complete question is 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 0.440 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 251.1 Hz. Measuring from the bottom of the pipe, what is the level of the water?

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