MCQ
A wave equation which gives the displacement along the $Y$ direction is given by the equation $y=10^4 \sin (60 t+2 x)$, where $x$ and $y$ are in metres and $t$ is time in seconds. This represents a wave
  • Travelling with a velocity of $30 \mathrm{~m} / \mathrm{sec}$ in the negative $X$ direction
  • B
    Of wavelength $\pi$ metre
  • C
    Of frequency $30 / \pi \mathrm{Hz}$
  • D
    Of amplitude $10^4$ metre travelling along the negative $X$ direction

Answer

Correct option: A.
Travelling with a velocity of $30 \mathrm{~m} / \mathrm{sec}$ in the negative $X$ direction
On comparing the given equation with $y=a \sin (\omega t+k x)$, it is clear that wave is travelling in negative $x-$ direction.It's amplitude $a=10 m$ and $\omega=60, k=2$.
Hence frequency $n=\frac{\omega}{2 \pi}=\frac{60}{2 \pi}=\frac{30}{\pi} \mathrm{Hz}$
$k=\frac{2 \pi}{\lambda}=2 $
$\Rightarrow \lambda=\pi \mathrm{m} $ and $ v=\frac{\omega}{k}=\frac{60}{2}=30 \mathrm{~m} / \mathrm{s}$

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