A wave equation which gives the displacement along y-direction is given by $y = 0.001 \sin(100t - x)$ where x and y are in meter and t is time in second. This represented a wave
(a) Of frequency $\frac{100}{\pi}$ Hz (b) Of wavelength one meter (c) Travelling with a velocity of $\frac{50}{\pi}$ ms$^{-1}$ in the positive X-direction (d) Travelling with a velocity of 100 ms$^{-1}$ in the negative X-direction
Text Solution
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Compare the given equation with
$y = a \sin(\omega t + kx)$ ⇒ ⇒ $\omega = 2 \pi m = 100$ ⇒ ⇒ $n = \frac{50}{\pi} \text{ Hz}$
$k = \frac{2 \pi}{\lambda} = 1$ ⇒ ⇒ $\lambda = 2 \pi$ and $\mathbf{v} = \omega / k = 100 \mathrm{m} / \mathrm{s}$
Since ‘+’ is given between t terms and x term, so wave is travelling in negative x-direction.
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