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A wave disturbance in a medium is described by `y(x, t) = 0.02 cos(50pit + (pi)/(2))cos(10pix)` where `x and y` are in meter and `t` is in second`A. A node occurs at `x = 0.15 m`B. An antinode occurs at `x = 0.3 m`C. The speed of wave is `5 m//s`D. The wave length is `0.2 m` |
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Answer» Correct Answer - A::B::C::D It is given that `y(x,t) = 0.02 cos (50 pi t + pi//2) cos (10 pi x)` `~= A cos (omega t + (pi)/(2)) cos kx` Node occurs when `kx = (pi)/(2),(3pi)/(2)`, etec `rArr 10 pi r = (pi)/(2),(3pi)/(2)` `rArr x = 0.05 m, 0.15 m` option (a) Anitnode occurs when `kx=pi,2pi,3pi` etc. `rArr 10 pix = pi, 2pi, 3pi` etc `rArr x = 0.1 m, 0.02 m, 0.3 m` option (b) Speed of the wave is given by `v=(omega)/(k) =(50 pi)/(10 pi)=5 m//s` option (c) Wavelength is given by `lamda=(2 pi)/(k)=(2pi)/(10 pi) =((1)/(5))m=0.2 m`. option (d). |
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