Question

The velocity of a travelling plane wave given by \[ y = 10^{-2} \sin \left( 200t - \frac{x}{5} \right) m, \] is

• A. $10 \, \text{m}^{-1}$
• B. $500 \, \text{m}^{-1}$
• C. $400 \, \text{m}^{-1}$
• D. $5 \, \text{m}^{-1}$
• E. $1000 \, \text{m}^{-1}$

Hint:

The speed of a wave is given by the ratio of its angular frequency $\omega$ to the wave number $k$.

Answer 1

Answer: (E)

Step 1: The standard form of a travelling wave equation is: \[ y = A \sin (\omega t - kx) \] where $\omega$ is the angular frequency, $k$ is the wave number, and the wave velocity $v$ is given by: \[ v = \frac{\omega}{k} \] Step 2: From the given equation, we compare terms: \[ \omega = 200, \quad k = \frac{1}{5} \] Step 3: Using the wave velocity formula: \[ v = \frac{200}{1/5} = 200 \times 5 = 1000 { ms}^{-1} \] Step 4: Therefore, the correct answer is (E).