Question

The equation of a wave is represented by :y=10^-4sin(100t-x/10)m,then the velocity of the wave will be:
a)100 m/s b)1000 m/s c)4 m/s d)10 m/s.

Answer 1

Answer on Question #38002, Physics, Other

Question:

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

a) $100 \, \text{m/s}$

b) $1000 \, \text{m/s}$

c) $4 \, \text{m/s}$

d) $10 \, \text{m/s}$

Answer:

Traveling sinusoidal wave is represented mathematically in terms of its velocity $v$ (in the $x$ direction) and wavenumber $k$ as:

$$y(x, t) = A \sin \left(k(x - vt)\right)$$

In our case equation of a wave is:

$$y = 10^{-4} \sin \left(100t - \frac{x}{10}\right) = 10^{-4} \sin \left(\frac{1}{10} (1000t - x)\right)$$

Therefore, velocity of wave equals:

$$v = 1000 \frac{m}{s}$$

Answer: b) $1000 \, \text{m/s}$