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Waves question

2013 · Q160
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Waves question

2013 · Q160

NEETPhysicsWavesMCQ+4 / −1
A wave travelling in the + ve x-direction having displacement along y-direction as 1 m, wavelength 2π\piπ m and frequency of 1π{1 \over \pi }π1​ Hz is represented by
  1. A
    y = sin(10π\piπx −-− 20π\piπt)
  2. B
    y = sin(2π\piπx + 2π\piπt)
  3. C
    y = sin(x −-− 2t)
  4. D
    y === sin(2π\piπx −-− 2π\piπt)
View written solutionFree

Correct answer: C

The standard equation of a wave travelling along +ve x-direction is given by

y=Asin(kx−ωt){\rm{y = Asin(kx - }}\omega {\rm{t)}}y=Asin(kx−ωt)

where A = Amplitude of the wave
k = angular wave number
ω\omega ω = angular frequency of the wave

Given: A = 1 m, λ=2πm,υ=1πHz\lambda = {\rm{2}}\pi m,\upsilon = {1 \over \pi }Hzλ=2πm,υ=π1​Hz

As k=2πλ=2π2π=1k = {{2\pi } \over \lambda } = {{2\pi } \over {2\pi }} = 1k=λ2π​=2π2π​=1

ω=2πυ=2π×1π=2\omega = 2\pi \upsilon = 2\pi \times {1 \over \pi } = 2ω=2πυ=2π×π1​=2

∴\therefore∴ The equation of the given wave is

y = 1 sin (1x – 2t) = sin(x – 2t)

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