Two sound waves (expressed in CGS units) given by y_1 = 0.3 2 (vt… - Vidyadip

MCQ

Two sound waves (expressed in $CGS$ units) given by ${y_1} = 0.3\sin \frac{{2\pi }}{\lambda }(vt - x)$ and ${y_2} = 0.4\sin \frac{{2\pi }}{\lambda }(vt - x + \theta )$ interfere. The resultant amplitude at a place where phase difference is $\pi /2$ will be .... $ cm$

A
$0.7$
B
$0.1$
✓
$0.5$
D
$\frac{1}{{10}}\sqrt 7 $

✓

Answer

Correct option: C.

$0.5$

c
(c) Resultant amplitude = $\sqrt {a_1^2 + a_2^2 + 2{a_1}{a_2}\cos \phi } $

= $\sqrt {{{0.3}^2} + {{0.4}^2} + 2 \times 0.3 \times 0.4 \times \cos \frac{\pi }{2}} $= $0.5\,\,cm$

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