Waves in Pipes and Strings

Waves in Pipes and Strings:

Organ Pipe:

A hollow tube which is used to produce sound by blowing air into it is called an organ pipe. It is wind instrument. There are two types of organ pipe which are as follows.

1. Closed Organ Pipe: The organ pipes whose one end is closed and another end is open is called a closed organ pipe. e.g. whistle, cap of pen, bottle, resonance tube etc. 2. Open Organ Pipe: The organ pipe whose both ends are open are called open organ pipe. e.g. flute, clarinet etc.

Stationary Waves in Closed Organ Pipe

When a blast of air is blown into the closed organ pipe through its open-end, longitudinal wave travels forward and gets reflected from the closed end. Due to superposition between ongoing and reflected waves longitudinal stationary wave is formed in the pipe. There is always a node at the closed end and an anti node at the open end. The lowest possible frequency of vibration in the organ pipe is called fundamental frequency and higher frequencies are called overtones. The various modes of vibration in closed organ pipes are as follows.

Fundamental Mode:

In the simplest mode of vibration, called fundamental mode in closed organ pipe, there is a node at closed end and an anti node at the open end. If λ1 be the wavelength of wave in the mode, then length L of the pipe can be expressed as

L=λ14

⟹ λ1 = 4L

Then, frequency of vibration in this mode is given by

f1=vλ1, where v is wave velocity or velocity of sound

∴f1=v4L

This is the expression for fundamental frequency in closed organ pipe called first harmonic.

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