NEET Physics Notes Waves-Standing or Stationary Waves
Standing or Stationary Waves
Standing or Stationary Waves
Standing or stationary wave is formed due to superposition of two progressive waves of same nature, same frequency (or same wavelength), same amplitude travelling with same speed in a bounded medium in mutually opposite directions.
The resultant wave does not represent a progressive wave.
Standing Waves in String
Consider a string of length L stretched under tension T between two fixed points (i.e. clamped at its ends). Transverse wave is set up on the string whose speed is given by 
where 
is the mass per unit length of the string. Let only one anti-node A is formed at the centre and string vibrates in one segment only, then
Frequency of vibration in fundamental mode
It is known as the fundamental frequency or first harmonic.- If string vibrates in two segments, then
It is known as first overtone or second harmonic. - Similarly, if the string vibrates in three segments, then
It is called second overtone or third harmonic - In general, if a string vibrates in p segments i.e. have (p + 1) nodes and p antinodes, then
and it is known as pth harmonic or (p – l)th overtone.
Standing Waves in Organ Pipes (Air Columns)
Organ pipes are those cylindrical pipes which are used for producing musical (longitudinal) sounds. The standing waves in both organ pipes (i.e. open organ pipe and closed organ pipe) are described below.
Open Organ Pipe
- As shown in figure anti-nodes are formed at both the open ends of pipe and one or more nodes are formed in between symmetricall y. The number of nodes is 1 less than the number of anti-nodes.
- In fundamental mode (1st harmonic) only one node is formed at the centre of pipe and so
- All harmonics are present in open pipe with their frequencies in the ratio 1:2:3:4…. and ratio of overtones = 2 : 3 : 4 : 5..
- Position of nodes from one end
- Position of anti-nodes from one end
Closed Organ Pipe
- Longitudinal stationary waves are formed such that open end of pipe behaves as an anti-node and a node is formed at the closed end.
- In fundamental mode,
- Fundamental (1st harmonic) frequency
- For a pipe of length L, the fundamental frequency in a closed pipe is half of that in open pipe. Thus,vopen = 2 x vclosed for fundamental mode.