The equations of two waves are given by: y1=5 sin 2 π(x-v t) cm y2=3 sin 2 π(x-v t+1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is

Question

The equations of two waves are given by: y1=5 sin 2 π(x-v t) cm y2=3 sin 2 π(x-v t+1.5) cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is (A) 2 cm (B) 4 cm (C) 5.8 cm (D) 8 cm

Tardigrade Admin · Accepted Answer

A 1=5 A 2=3 Δ θ=2 π(1.5)=3 π A text net =√ A 12+ A 22+2 A 1 A 2 cos (3 π) =| A 1- A 2| =2 cm

Q. The equations of two waves are given by:
$y_{1} = 5 sin 2 π (x - v t) c m$
$y_{2} = 3 sin 2 π (x - v t + 1.5) c m$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is

$2 c m$

$4 c m$

$5.8 c m$

$8 c m$

$A_{1} = 5 A_{2} = 3$
$Δ θ = 2 π (1.5) = 3 π$
$A_{net} = A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos (3 π)$
$= ∣ A_{1} - A_{2} ∣$
$= 2 c m$

Q. The equations of two waves are given by: y1​=5sin2π(x−vt)cm y2​=3sin2π(x−vt+1.5)cm These waves are simultaneously passing through a string. The amplitude of the resulting wave is

2cm

4cm

5.8cm

8cm