If two waves- originating from sources represented by y1 - 4 sin - t and y2 - 3 sin- t - -3 interfere at a point- The amplitude of that point will be about-

The equations of the sources are nbsp;y_1 = 4 sin (ω t ) and y_2 = 3 sin(ω t + π3) So, both the sources are coherent. ∴ The resultant amplitude at the given p ...

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Standard XII

Physics

Sound Wave:Displacement Equation

If two waves,...

Question

If two waves, originating from sources represented by $y_{1} = 4 sin (ω t)$ and $y_{2} = 3 sin (ω t + \frac{π}{3})$ interfere at a point. The amplitude of that point will be about,

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Solution

The correct option is B $6$
The equations of the sources are $y_{1} = 4 sin (ω t)$ and $y_{2} = 3 sin (ω t + \frac{π}{3})$
So, both the sources are coherent.
$∴$ The resultant amplitude at the given point is,

$A = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos ϕ}$
Here, $A_{1} = 4$
$A_{2} = 3$
$ϕ = \frac{π}{3}$
$∴ A = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos ϕ}$

$= \sqrt{4^{2} + 3^{2} + 2 \times 4 \times 3 cos (\frac{π}{3})}$

$= \sqrt{16 + 9 + 24 \times \frac{1}{2}} = \sqrt{37} \approx 6$

Hence, $(B)$ is the correct answer.

$\begin{matrix} Why this question? To understand the concept of interference and calculation of amplitude of resultant wave. \end{matrix}$

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If two waves, originating from sources represented by y1=4sin(ωt) and y2=3sin(ωt+π3) interfere at a point. The amplitude of that point will be about,

If two waves, originating from sources represented by $y_{1} = 4 sin (ω t)$ and $y_{2} = 3 sin (ω t + \frac{π}{3})$ interfere at a point. The amplitude of that point will be about,