The equations of two waves are given by : \[ \begin{aligned} & \mathrm{y}_{1}=5 \sin 2 \pi(\mathrm{x}-\mathrm{vt}) \mathrm{cm} \\ & \mathrm{y}_{2}=3 \sin 2 \pi(\mathrm{x}-\mathrm{vt}+1.5) \mathrm{cm} \end{aligned} \] These waves are simultaneously passing through a string. The amplitude of the resulting wave is

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Waves & Sound

The equations of two waves are given by :

y_{1} = 5 sin 2 π (x - vt) cm y_{2} = 3 sin 2 π (x - vt + 1.5) cm

These waves are simultaneously passing through a string. The amplitude of the resulting wave is

Answer: (A)

The amplitudes are

A_{1} = 5

cm and

A_{2} = 3

cm.

Phase difference:

Δ θ = 2 π (1.5) = 3 π

Resultant amplitude:

A_{net} = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos (3 π)

Since

cos (3 π) = - 1

A_{net} = 25 + 9 - 30 = 4 = 2 cm

Alternatively,

A_{net} = ∣ A_{1} - A_{2} ∣ = ∣5 - 3∣ = 2

cm (destructive interference)

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Single correct option