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

A1=5 A2=3 Δθ=2π(1.5)=3π Anet=A12+A22+2A1A2cos⁡(3π) =|A1−A2| =2cm

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

A1=5 A2=3 Δθ=2π(1.5)=3π Anet=A12+A22+2A1A2cos⁡(3π) =|A1−A2| =2cm

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The equations of two waves are given by :
$\begin{aligned} y_{1} = 5 \sin 2 π (x - vt) cm \\ y_{2} = 3 \sin 2 π (x - vt + 1 .5) cm \end{aligned}$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is

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5.8 cm

8 cm

2 cm

4 cm

answer is A.

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$\begin{aligned} A_{1} = 5 A_{2} = 3 \\ Δ θ = 2 π (1.5) = 3 π \\ A_{net} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} \cos (3 π)} \\ = | A_{1} - A_{2} | \\ = 2 cm \end{aligned}$

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

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The equations of two waves are given by :
$\begin{aligned} y_{1} = 5 \sin 2 π (x - vt) cm \\ y_{2} = 3 \sin 2 π (x - vt + 1 .5) cm \end{aligned}$
These waves are simultaneously passing through a string. The amplitude of the resulting wave is