The equations of motion of two waves propagating in the same direction in a medium is given by y 1- A sin - t - kx and y2-A sin - t-k x-Then amplitude of the particle in this medium isA- -2 A cos-2B- 2 A cos-2C- -2 A cos-D- 2 A cos-

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Byju's Answer

Standard XII

Physics

Resultant Amplitude

The equations...

Question

The equations of motion of two waves propagating in the same direction in a medium is given by
$y_{1} = A s i n (ω t - k x)$
and $y_{2} = A s i n (ω t - k x - θ)$ .
Then amplitude of the particle in this medium is

\sqrt{2} A c o s θ

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2 A c o s θ

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\sqrt{2} A c o s \frac{θ}{2}

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2 A c o s \frac{θ}{2}

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Solution

The correct option is D $2 A c o s \frac{θ}{2}$
Resultant amplitude when waves of phase difference $θ$ , interfere is given by
$y_{0} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} (c o s θ)}$
Here $A_{1} = A_{2} = A$

$\Rightarrow y_{0} = A \sqrt{2 (1 + c o s θ)} = 2 A c o s \frac{θ}{2}$

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The equations of motion of two waves propagating in the same direction in a medium is given by y1=A sin(ωt−kx) and y2=A sin(ωt−kx−θ). Then amplitude of the particle in this medium is

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The equations of motion of two waves propagating in the same direction in a medium is given by
$y_{1} = A s i n (ω t - k x)$
and $y_{2} = A s i n (ω t - k x - θ)$ .
Then amplitude of the particle in this medium is

The correct option is D $2 A c o s \frac{θ}{2}$
Resultant amplitude when waves of phase difference $θ$ , interfere is given by
$y_{0} = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} (c o s θ)}$
Here $A_{1} = A_{2} = A$

$\Rightarrow y_{0} = A \sqrt{2 (1 + c o s θ)} = 2 A c o s \frac{θ}{2}$