Question

A plane wave is represented, in usual symbols, by the equation, \(y=2 \sin \pi \left(200t - \dfrac{x}{150}\right).\) Its frequency
1. 2 Hz
2. 100 Hz
3. 150 Hz
4. 200 Hz

Answer 1

Correct Answer - Option 2 : 100 Hz

CONCEPT:

• A plane wave is a special kind of wave associated with infinite parallel plane wavefronts.  
• A plane wave has a constant frequency.
• Mathematically it is written as

⇒ y = a sin(ωt - kx)     ------ (1)

Where a = amplitude, ω = angular frequency, \(f = \frac{\omega}{2\pi}\) = frequency, and k = wave vector associated with the plane wave.

EXPLANATION:

• Equation of the wave is given as:

\(\Rightarrow y=2 \sin \pi \left(200t - \dfrac{x}{150}\right)\)    ------ (2)

• On comparing the above two equations, we get

⇒ ω = 200π

• As we know, the relation between angular frequency and linear frequency is given by

\(⇒ f = \frac{\omega}{2 \pi} = \frac{200 \pi }{2 \pi} = 100 Hz\)

• Therefore option 2 is correct.