The equation of a wave is represented by y=10-4 sin ( 100t-(x/10) )m, the velocity of the wave will be

Question

The equation of a wave is represented by y=10-4 sin ( 100t-(x/10) )m, the velocity of the wave will be (A)  0.1 text ms-1  (B)  10 text ms-1  (C)  100 text ms-1  (D)  1000 text ms-1

Tardigrade Admin · Accepted Answer

The given equation comparing with standard equation y=A sin (2π /λ )(vt-x) ∴ (2π /λ )v=100 and (2π /λ )=(1/10) ⇒ v=1000 text ms-1

Q. The equation of a wave is represented by $y = 10^{- 4} sin (100 t - \frac{x}{10}) m,$ the velocity of the wave will be

$0.1 m s^{- 1}$

$10 m s^{- 1}$

$100 m s^{- 1}$

$1000 m s^{- 1}$

The given equation comparing with standard equation
$y = A sin \frac{2 π}{λ} (v t - x)$
$∴$ $\frac{2 π}{λ} v = 100$
and $\frac{2 π}{λ} = \frac{1}{10}$
$\Rightarrow$ $v = 1000 m s^{- 1}$

Q. The equation of a wave is represented by y=10−4sin(100t−10x​)m, the velocity of the wave will be

0.1ms−1

10ms−1

100ms−1

1000ms−1