Question

If a progressive wave is represented as \[ y = 2 \sin \left( \pi \left( \frac{t}{2} - \frac{x}{4} \right) \right) \] where \( x \) is in meters and \( t \) is in seconds, then the distance traveled by the wave in 5 s is

• A. 5 m
• B. 10 m
• C. 25 m
• D. 32 m

Hint:

The speed of a wave is calculated by dividing the angular frequency by the wave number.

Answer 1

The Correct Option is B

Step 1: Wave equation analysis.
The general form of a progressive wave is \( y = A \sin(kx - \omega t) \), where \( k \) is the wave number, \( \omega \) is the angular frequency, and \( v = \frac{\omega}{k} \) is the wave speed. In this case, comparing with the given equation, we find the wave speed \( v = 8 \, \text{m/s} \).

Step 2: Distance traveled in 5 seconds.
The distance traveled by the wave is given by \( d = v \cdot t \), where \( t = 5 \, \text{s} \). Hence, the wave travels 10 m.