Question

The equation of a wave is $y=5\sin (\frac{t}{0.04}-\frac{x}{4})$ ; where, $x$ is in $cm$ and $t$ is in second. The maximum velocity of the wave will be

• A. $1m{s}^{-1}$
• B. $2m{s}^{-1}$
• C. $1.5m{s}^{-1}$
• D. $1.25m{s}^{-1}$

Answer 1

Answer: (D)

Equation of wave $y=5\sin (\frac{t}{0.04}-\frac{x}{4})$
The standard equation of a wave in the given form is
$y=a\sin (\omega t-\frac{2\pi x}{\lambda })$
Comparing the given equation with the standard equation, we get
$a=5$ and $\omega =\frac{1}{0.04}=25$
Therefore, maximum velocity of particles of the medium.
$v_{max}=a\omega =5\times 25=125cm{s}^{-1}=1.25m{s}^{-1}$