A plane progressive wave is given by y=2 cos 2 π(330 t-x) m. The frequency of the wave is :

Solution

Physics sir · 3 steps

Match the bracket to ω t - kx: the 2π outside is already your 2π f.

1. Standard form. A travelling wave can be written as y = A cos(ω t - kx), where ω = 2π f is the angular frequency.
2. Open the bracket. Multiply the 2π through: y = 2 cos(2π × 330 t - 2π x). So the coefficient of t is ω = 2π × 330 rad s⁻¹.

   f = ω/2π = (2π × 330)/2π = 330 Hz

3. So. The frequency is 330 Hz, option (c).

The idea to keep. Always read ω as the full coefficient of t inside the cosine, then divide by 2π. If the form is 2π(ft - x/λ), the number with t is f itself.

Answer from the NTA final answer key. Solution by PrepWiser.