A standing wave having 3 nodes and 2 antinodes is formed between two atoms having a distance 1.21 Å between them. The wavelength of the standing wave is :
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In stationary waves, the distance between a node and its nearest antinode is 20 cm. The phase difference between two particles having a separation of 60 cm will be :
, also
⇒
A standing wave is represented by
where Y and A are in millimetre, t is in seconds and x is in metre. The velocity of the wave is :
By comparing given equation with
⇒
Two waves are approaching each other with a velocity of 20 m/s and frequency n. The distance between two consecutive nodes is :
Distance between the consecutive node
but so
The stationary wave produced on a string is represented by the equation where x and y are in cm and t is in seconds. The distance between consecutive nodes is :
On comparing the given equation with standard equation .
Hence, distance between two consecutive nodes ⇒ λ = 3 cm
The following equations represent progressive transverse waves , , and . A stationary wave will be formed by superposing :
When two waves of equal frequency and traveling in the opposite direction superimpose, then the stationary wave is produced. Hence Z1 and Z2 produce stationary waves.
Two traveling waves and are superimposed on the string. The distance between adjacent nodes is :
The distance between adjacent nodes
Also,
Hence,
A string fixed at both ends is vibrating in two segments. The wavelength of the corresponding wave is :
When a string fixed at both ends vibrates in two segments, it means there is one node at the center. The wavelength of the standing wave is twice the length of the string segment, which is equal to the full length of the string (l).
A 1 cm long string vibrates with the fundamental frequency of 256 Hz. If the length is reduced to keeping the tension unaltered, the new fundamental frequency will be :
⇒
⇒
Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is :
String vibrates in five segment so ⇒
Hence
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