Match the standing waves formed in column – II due to plane progressive waves in Column – I and also with conditions in column - I
Column-I | Column-II |
(i) Incident wave is y = A sin (kx –ωt) | [A] y = 2A cos kx sin ωt |
(ii) Incident wave is y = A cos (kx –ωt) | [B] y = 2A sin kx cos ωt |
(iii) x = 0 is rigid support | [C] y = 2A sin kx cos ωt |
(iv) x = 0 is flexible support | [D] y = 2A cos kx cos ωt |
Text Solution
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Ans.
(i) [A],[C]
(ii) [B],[D]
(iii) [B],[C]
(iv) [A],[D]
Sol.
y 1 = A sin (kx – ω t)
y 2 = A sin (kx + ω t)
y = y 1 + y 2 = 2A sin kx cos ω t
y 1 = A sin (kx – ω t)
y 2 = –A sin (kx + ω t)
y = y 1 + y 2 = 2A cos kx sin ω t
y 1 = A cos (kx – ω t)
y 2 = A cos (kx + ω t)
y = y 1 + y 2 = 2A cos kx cos ω t
y 1 = A cos (kx – ω t)
y 2 = –A cos (kx + ω t)
y = y 1 + y 2 = 2A sin kx sin ω t
x = 0, rigid support i.e., nodes is
At nodes y = 0. This is satisfied by equations –
y = 2 A sin kx cos ω t
and y = 2 A sin kx sin ω t
x = 0, flexible support i.e., antinodes
At antinodes y is maximum. This is satisfied by equations –
y = 2A cos kx sin ω t
and y = 2A cos kx cos ω t.
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