The displacement equation of a standing wave in air is given by
y = A cos kx cos ωt
Match the physical quantities (Z) in the column-I, to the correct plots in the column-II
Column-I | Column-II |
(i) Displacement y of the particles at t = T/2 | [A] |
(ii) Velocity of the particles at t = T/4 | [B] |
(iii) Change in pressure of the medium at t = 0 | [C] |
(iv) Density of the medium at t = T/2 | [D] |
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
Ans.
(i) [C]
(ii) [C]
(iii) [D]
(iv) [B]
Sol.
(i) y = A cos kx cos 
× T/2 = – A cos kx (at t = T/2)
Hence plot is (R)
(ii) v p = 
= – A ω cos kx sin ω t = – A ω cos kx sin π /2
= – A ω cos kx (at t = T/4
Hence plot is (R)
(iii) Δ P = – B 
= + BkA sin kx cos ω t
= + BkA sin kx (at t = 0) Hence plot is (S)
(iv) Pressure at any point 
Δ P = (BAk) sin kx
Density 
ρ = 
[P 0 ± Δ P]
ρ = ρ 0 ± Δρ
= ρ 0 ± 
Δ P
= ρ 0 ± 
[–(BAk) sin kx] at (t = T/2)
ρ = ρ 0 ± 
(– sin kx) where 
= Bak
Hence plot is (Q)
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