What are the characteristics of stationery waves? Give the laws of transverse vibrations in a stretched string.

Explanation

1.Stationary waves are characterised.by the confinement of a wave disturbance between two rigid boundaries. This means, the wave does not move forward or backward in a medium (does not advance), it remains steady at its place. Therefore, they are called ·.stationary waves or standing waves"
2. Certain points in the region in which the wave exists have maximum amplitude, called as anti-nodes and at certain points the amplitude is minimum or zero, called as nodes
3. The distance between two consecutive nodes (or) anti-nodes is `lamda/2`
4. The distance between a node and its neighbouring anti-node is `lamda / 4`
5. The transfer of energy along the standing wave is zero.
Laws of transverse vibrations in stretched strings: There are three laws of transverse vibrations of stretched strings which are given as follows:
(i) The law oflength: For a given wire with tension T (which is fixed) and mass per unit length `mu` (fixed) the frequency varies inversely with the vibrating length. Therefore,
` f prop 1/l rArr f = C/l`
` rArr l xx f = C` , where C is a constant
(ii) The law of tension: For a given vibrating length l (fixed) and mass per unit length `mu` (fixed) the frequency varies directly with the square root of the tension T,
` f prop sqrtT`
` rArr f = A sqrtT` , where A is a constant
(iii) The law of mass: For a given vibrating length l (fixed) and tension T (fixed) the frequency varies inversely with the square root of the mass per unit length `mu` ,
` f prop (1)/(sqrt mu) ` , where B is a constant