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

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1.5 cm

2.5 cm

2 cm

3 cm

answer is B.

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Detailed Solution

A₁= 5, A₂= 3,

Phase difference,

$∆ \emptyset = 2 π (1.5) = 3 π$

A_net = $\sqrt{{A_{1}}^{2} + {A_{2}}^{2} + 2 A_{1} A_{1} \times c o s 3 π}$

A_net = $\sqrt{5^{2} + 3^{2} + 2 \times 5 \times 3 \cos (3 π)} = \sqrt{4} = 2 c m$

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