Question

Equation of progressive wave is given by $y=a \, \sin\,\pi(40t-x)$ where $a$ and $x$ are in metre and $t$ in second. The velocity of the wave is (m/s)

• A. 40
• B. 10
• C. 80
• D. 20

Answer 1

Answer: (A)

40

Answer 2

Comparing the given equation with standard equation $y = a \, sin (\omega t - kx)$ ,
we get $\omega$ = 40 $\pi$ i.e. $2 \pi f = 40 \pi$ i.e. $f$ = 20 per s
And $k = \pi$ i.e. $\frac{2 \pi}{\lambda} = \pi$ i.e. $\lambda$ = 2 m
$\upsilon = \int \, \lambda = 20 \times 2 = 40 \, m \, s^{-1}$