Question

The equation of a simple harmonic progressive wave is given by y = 0.05 (100 t - 0.4 x), where x and y are in meters and t is in seconds. The wave velocity is:

• A. 250 ms^-1
• B. 100 ms^-1
• C. 50 ms^-1
• D. 25 ms^-1

Hint:

For any wave equation given in the standard sinusoidal format, you can find the wave velocity instantly without full conversion steps using this simple ratio rule: Here, Velocity = 1000.4 = 250 ms^-1.

Answer 1

The Correct Option is A

Step 1: Read the wave equation.
The wave is $y = 0.05\,\sin(100t - 0.4x)$. We compare it with the standard form $y = A\,\sin(\omega t - kx)$ to pick out its parts.

Step 2: Find the angular frequency.
The number multiplying $t$ is the angular frequency. So $\omega = 100$ rad/s. This tells how fast the oscillation goes up and down.

Step 3: Find the wave number.
The number multiplying $x$ is the wave number. So $k = 0.4$ per metre. This tells how the wave is spread out in space.

Step 4: Recall the speed formula.
For a travelling wave, the speed is the angular frequency divided by the wave number: $v = \dfrac{\omega}{k}$.

Step 5: Put the values in.
\[ v = \frac{100}{0.4}. \]

Step 6: State the answer.
Dividing gives the wave velocity. \[ \boxed{250 \ \text{m s}^{-1}} \]