Question

The equation of simple harmonic progressive wave is given by y = A sin (100πt − 4x). The distance between two particles having a phase difference of `(pi/4)^c` is ______.

पर्याय

• `pi/18 m`

• `pi/16 m`

• `pi/9 m`

• `pi/3 m`

Answer 1

The equation of simple harmonic progressive wave is given by y = A sin (100πt − 4x). The distance between two particles having a phase difference of `(pi/4)^c` is `bbunderline(pi/16 m)`.

Explanation:

Equation of the given harmonic progressive wave:

y = A sin (100πt − 4x)    ...(i)

General equation of a harmonic wave:

y = A sin (ωt + kx)    ...(ii)

From equations (i) and (ii),

ω = 100π

k = 4

But, k = `(2 pi)/lambda`

⇒ 4 = `(2 pi)/lambda`

∴ λ = `pi/2`

We also know,

Path difference (Δx) = `lambda/(2 pi) xx "Phase difference" Delta Phi`

∴ Δx = `pi/(2 xx 2 pi) xx pi/4`    ...(Given: ΔΦ = `pi/4`)

= `pi/16 m`