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

Answer: (C)

$\frac {π}{9}$

Answer 2

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) $\frac {π}{9}$.