Question

Find the velocity of wave given by \( y = 0.05 \sin \left( \frac{2\pi}{\lambda} (x - 200t) \right) \).

Hint:

The velocity of a wave can be extracted from the wave equation by identifying the coefficient of \( t \) in the term \( (x - vt) \).

Answer 1

Step 1: General form of wave equation.
The general form of a wave equation is: \[ y = A \sin \left( \frac{2\pi}{\lambda} (x - vt) \right) \] where:
- \( A \) is the amplitude,
- \( \lambda \) is the wavelength,
- \( v \) is the wave velocity,
- \( t \) is the time, and
- \( x \) is the position.
In the given wave equation \( y = 0.05 \sin \left( \frac{2\pi}{\lambda} (x - 200t) \right) \), comparing with the general form, we have: \[ v = 200 \, \text{m/s} \]
Step 2: Velocity of the wave.
Thus, the velocity of the wave is: \[ v = 200 \, \text{m/s} \]