Krishna
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Every pressure wave produces a sound of some kind. But we call those kinds of sounds noise. If you want a clear, pure tone, then you need a resonator to amplify the “good” parts of the sound and suppress the “bad” parts. That’s what an organ pipe or a vibrating string is: a resonator. The standing wave represents the wavelength that the resonator is tuned to accept and reinforce.


Musical sounds can be produced by oscillating strings, air columns, membrane, steel bars and many other oscillating bodies. In most of the instruments, more than a single part take part in oscillation such as strings and body f violin vibrate producing musical sound.


Organ Pipe

A hollow wooden or metallic tube used to produce sound is called an organ pipe. It is wind instrument such as a flute, whistle, violin, clarinet etc. their air column in it set into vibrations by blowing air into it from one end. If both ends of the pipe are open, it is called an open organ pipe; flute is an example pipe.

figure afigure a

figure bfigure b

Figure (a) is a closed organ pipe. When air is blown from the mouthpiece M, a jet of air strikes a sharp edge L oscillating the air there and progressive sound waves travel along the pipe towards the closed end. The waves are reflected from the end and the reflected waves interfere with incident waves producing stationary waves in the pipe. Sound waves of other frequencies die out, so organ pipe can produce notes of definite frequencies depending on its length. Stationary waves are formed in an open pipe as shown in figure (b) due to reflection at the open end.


Stationary Waves in a Closed Organ Pipe


Consider a closed organ pipe of length L as shown in the figure (a). A blast of air is blown into it at the open end and a wave thus travels through the pipe and is reflected at the next end. Due to a superposition of incident and reflected waves, stationary waves are produced. In the simplest mode of vibration, there is a displacement node, N at the closed end air is at rest there and a displacement antinode, An at the open end as the air can vibrate freely.


Fundamental Mode


In this mode of vibration, the pipe has one node at its closed end and one antinode at its open end. As observed in figure (a), the length, L of the pipe is equal to distance between a node and an antinode which is λ/4 where λ is the wavelength of the stationary wave. Then

It is the lowest frequency produced in the pipe. It is called fundamental frequency or first harmonic.

Overtones in Closed Pipe

If a stronger blast of air is blown into the pipe, the notes of higher frequencies are obtained. The two nodes of vibration in the same pipe as shown in the figure which is called the first overtone and second overtone.


Conclusions
  1. The frequencies of various harmonics are odd integral multiples of fundamental frequency.
  2. The frequency of the first overtone is three times the fundamental frequency, frequency of the second overtone is five times the fundamental frequency. So the frequency of nth overtone is (2n + 1) times the fundamental frequency.
  3. The even harmonics are missing.
  4. Since only odd harmonics are present, the sound quality is poor.