Question

The maximum transverse velocity and maximum transverse acceleration of a harmonic wave in a one-dimensional string are $1 \, ms^{-1}$ and $1 \, ms^{-2}$ respectively. The phase velocity if he wave is $1\, ms^{-1}.$ The waveform is the wave is $1 \, ms^{-1}$. The waveform is

• A. $\sin (x - t) $
• B. $\sin (2x - t) $
• C. $\sin (x -2 t) $
• D. $\sin (x/2 - t) $
• E. $\sin (x - t/2) $

Answer 1

Answer: (A)

$\because$ Wave equation, $y=A_{0} \sin (k x-\omega t)$ ...(i)
where, $k=$ angular wave number $=\frac{2 \pi}{\lambda}$
$A_{0}=$ amplitude
$\because v_{\max }=a \omega$
$\therefore \omega=1$
$\left(\because\right.$ given that $\left. v_{\max }=1 \frac{m}{s}, a=1 \frac{m}{s^{2}}\right)$
$\because k=1$ (given)
$\therefore $ From Eq. (i), $y=\sin (x-t)$