Question

Standing wave produce in pipe closed at one end. The length of the pipe is (neglect end correction)

a) Odd integral multiple of

2

b) Even integral multiple of

2



c) Odd Integral multiple of

4

d) Even Integral multiple of

4

​

Answer 1

Answer:

The Physics of sound in tubes

This part of the Physics of sound is the basis of all wind instruments, from the piccolo to the organ. Basically the ideas are very simple but they can become complex for a specific musical instrument. For that reason we will confine ourselves to a general treatment of the production of a note from a uniform tube.

The stationary waves set up by the vibrations of the air molecules within the tube are due to the sum of two travelling waves moving down the tube in opposite directions. One of these is the initial wave and the other its reflection from the end of the tube.

All air-filled tubes have a resonant frequency and if the air inside them can be made to oscillate they will give out a note at this frequency. This is known as the fundamental frequency or first harmonic.

Higher harmonics or overtones may also be obtained and it is the presence of these harmonics that gives each instrument its individual quality. A note played on a flute will be quite unlike one of exactly the same pitch played on a bassoon!

A harmonic is a note whose frequency is an integral multiple of the particular tube's or string's fundamental frequency.

Tubes in musical instruments are of two types:

(a) open at both ends, or

(b) open at one end and closed at the other.

The vibration of the air columns of these types of tube in their fundamental mode are shown in Figure 1. Notice that the tubes have areas of no vibration or nodes at their closed ends and areas of maximum vibration or antinodes at their open ends.

An antinode also occurs at the centre of a tube closed at both ends in this mode.

Nodes are areas where the velocity of the molecules is effectively zero but where there is a maximum variation in pressure, while the reverse is true for antinodes.

Some of the higher harmonics for the different tubes are shown in Figure 2. Notice that a closed tube gives odd-numbered harmonics only, while the open tube will give both odd and even-numbered.

Explanation:

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