Question

An equation of a simple harmonic progressive wave is given by y = A sin (100πt-3x).The distance between two particles having a phase difference of \(\frac {π}{3}\) in metre is

• A. \(\frac {π}{3}\)
• B. \(\frac {π}{18}\)
• C. \(\frac {π}{9}\)
• D. \(\frac {π}{6}\)

Answer 1

The Correct Option is C

The general equation for a wave is y = A sin(kx - ωt) 
Comparing this equation to the given equation, we have: 
k = 3 
ω = 100π 
In this case, we are given a phase difference of \(\frac {π}{3}\). The general equation for the phase difference in terms of the wave number and wavelength is: 
Δϕ = k.Δx 
To find the distance between two particles with a phase difference of \(\frac {π}{3}\), we need to find Δx such that: 
k.Δx = \(\frac {π}{3}\) 
Substituting the value of k = 3, we have: 
3.Δx = \(\frac {π}{3}\) 
To isolate Δx, we divide both sides by 3: 
Δx = \(\frac {π}{9}\) 
Therefore, the distance between two particles with a phase difference of \(\frac {π}{3}\) is \(\frac {π}{9}\) meters. 
So, the correct option is (C) \(\frac {π}{9}\).