Stationary waves

Material Wave and Sound

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Stationary waves

(vi) For the positions of antinodes:

or x = even multiple of

(vii) Nodes: At these point the amplitude of particles is minimum and the change in pressure and density is maximum.

A_min = a₁ - a₂

or x = odd multiple of

13. For stationary waves:

1. waves produce nodes antinodes at regular points in limited medium .

2.The distance between to consecution nodes antinodes is 2 / 2

3.Distance between a node and as adjoient antinode is 2 / 4.

4. particles situated between two nodes execute simple harmonic motion whose amplitude are different but frequency are same .

5. Amplitude depends on the position of the particle , maximum amplitude is obtained at antinodes and zero amplitudes at the nodes .

6.The particles situated between two consecutive nodes vibrate in the phase with different amplitudes while the particles situated on either side of a node vibrate in the opposite phase .

14. Vibrations is a stretched string:

1. Transverse progressive wave is produced is a stretched string .

2.node is always formed at fixed and of string .

3.Velocing of the waves produced in a stretched string is

where t = tension and m = mass perurit length of string

If the density of material of string is d, radius is r, then

and if T = Mg.

(4) For a string fixed at both the ends, nodes are formed at the ends.

(5) If the length of a string is L & p loops are formed in it , then the frequency of the string

in the condition string is only loop. n₁is colled the fundamental frequency. This is also called first harmonic .

(b) If p = 2, then

In this condition n₂ is called the second harmonic or the first overtone.

= 3n₁, n₃ is called third harmonic or the second overtone.

(d) In the strings all harmonics are produced and their ratio is

n₁:n₂:n₃ ...... = 1:2:3:.....

(e) Some harmonics are shown in the figure .

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