Question

The equation of a wave is $y=5sin(\frac{t}{0.04}-\frac{x}{4})$ 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)

$1.25m{s}^{-1}$

Equations of wave $y=5sin(\frac{t}{0.04}-\frac{x}{4})$
The standard equation of a wave in the given from is
$y=asin(\omega t-\frac{2\pi x}{\lambda })$
Comparing the given equation with the standard equation, we get
$a=5$
and $\omega =\frac{1}{0.04}=25$and $\lambda =8\pi$
Therefore, maximum velocity of particles of the medium.
$v_{max}=a\omega =5\times 25$
$=125cs{m}^{-1}$
$=1.25m{s}^{-1}$