Waves

JEE Main level, single correct, medium

45 of 142

Question 45 of 142

A wave travelling along the xx-axis is described by the equation y(x,t)=0.005cos⁡(αx−βt)y(x, t)=0.005 \cos (\alpha x-\beta t). If the wavelength and the time period of the wave are 0.08 m0.08 \mathrm{~m} and 2.0 s2.0 \mathrm{~s}, respectively, then α\alpha and β\beta in appropriate units are

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Answer: (A) α=25.00π,β=π\alpha=25.00 \pi, \beta=\pi

y=0.005cos⁡(αx−βt)y=0.005 \cos (\alpha x-\beta \mathrm{t})
comparing the equation with the standard form,
y=Acos⁡[(xλ−tT)2π]2π/λ=α and 2π/T=βα=2π/0.08=25.00πβ=π\begin{aligned} & y=A \cos \left[\left(\frac{\mathrm{x}}{\lambda}-\frac{\mathrm{t}}{\mathrm{T}}\right) 2 \pi\right] \\ & 2 \pi / \lambda=\alpha \text { and } 2 \pi / T=\beta \\ & \alpha=2 \pi / 0.08=25.00 \pi \\ & \beta=\pi \end{aligned}

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