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Home » A transverse harmonic wave on a wire is expressed as: (i) Is it a stationary wave or a travelling one?ii) If it is a travelling wave, give the speed and direction of its propagation.[ and are in and in seconds. Assume the left to right direction as the positive direction of
A transverse harmonic wave on a wire is expressed as: y(x, t)=3 \sin (36 t+0.018 x+\pi / 4)
(i) Is it a stationary wave or a travelling one?
ii) If it is a travelling wave, give the speed and direction of its propagation.
[\mathrm{x} and \mathrm{y} are in \mathrm{cm} and \mathrm{t} in seconds. Assume the left to right direction as the positive direction of \mathrm{x}]
CBSE | Class 11 | NCERT | Physics | Waves
A transverse harmonic wave on a wire is expressed as: y(x, t)=3 \sin (36 t+0.018 x+\pi / 4)
(i) Is it a stationary wave or a travelling one?
ii) If it is a travelling wave, give the speed and direction of its propagation.
[\mathrm{x} and \mathrm{y} are in \mathrm{cm} and \mathrm{t} in seconds. Assume the left to right direction as the positive direction of \mathrm{x}]

Given function is,

(x, t)=3 \sin (36 t+0.018 x+\pi / 4)

i) The equation of a progressive wave travelling from right to left is known as,

y(x, t)=a \sin (\omega t+k x+\Phi)

On comparing equation (1) and equation (2), we see that it represents a wave travelling from right to left, and,

\mathrm{a}=3 \mathrm{~cm}, \omega=36 \mathrm{rad} / \mathrm{s}, \mathrm{k}=0.018 \mathrm{~cm} \text { and } \phi=\pi / 4

ii) As a result, the speed of propagation will be,

v=\omega / k=36 / 0.018=20 \mathrm{~m} / \mathrm{s}

i

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