Equations of motion in the same direction are given by- y1 - a sin - t - kx y2 - a sin - t - kx - -The amplitude of the medium particle will be-

The correct option is A 2acosθ/2 [ The resultan ...

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Standard XII

Physics

Wave Equation

Equations of ...

Question

Equations of motion in the same direction are given by:
$y_{1} = a s i n (ω t - k x)$
$y_{2} = a s i n (ω t - k x - θ)$
The amplitude of the medium particle will be:

2 a cos \frac{θ}{2}

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\sqrt{2} a c o s θ

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4 a c o s θ / 2

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\sqrt{2} a c o s θ / 2

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Solution

The correct option is A $2 a cos \frac{θ}{2}$
$\begin{matrix} T h e r e s u l tan t a m p l i t u d e i s g i v e n b y a_{R} = \sqrt{a^{2} + a^{2} + 2 \cdot a \cdot a cos θ} = \sqrt{2 a^{2} (1 + cos θ)} = 2 a cos \frac{θ}{2} (H cos θ = 2 {cos}^{2} \frac{θ}{2}) \end{matrix}$
Hence,
option $(A)$ is correct answer.

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Equations of motion in the same direction are given by:y1=a sin (ωt−kx)y2=a sin (ωt−kx−θ)The amplitude of the medium particle will be:

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