Two waves are propagating to the point P along a straight line pr… - Vidyadip

MCQ

Two waves are propagating to the point $P$ along a straight line produced by two sources $A$ and $B$ of simple harmonic and of equal frequency. The amplitude of every wave at $P$ is ' $a$ ' and the phase of $A$ is ahead by $\frac{\pi}{3}$ than that of $B$ and the distance $A P$ is greater than $B P$ by $50 \mathrm{~cm}$. Then the resultant amplitude at the point $P$ will be, if the wavelength is 1 meter

A
$2 a$
B
$a \sqrt{3}$
C
$a \sqrt{2}$
✓
$a$

✓

Answer

Correct option: D.

$a$

(d) Path difference$(\Delta x)=50 \mathrm{~cm}=\frac{1}{2|}\mathrm{~m} $
$\therefore \text { Phase difference } \Delta \phi=\frac{2 \pi}{\lambda} \times \Delta x \Rightarrow \phi=\frac{2 \pi}{1} \times \frac{1}{2}=\pi $
Total phase difference $=\pi-\frac{\pi}{3}=\frac{2 \pi}{3} $
$\Rightarrow A=\sqrt{a^2+a^2+2a^2\cos(2\pi3)}=a$

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