First slide

Interference

Question

Three waves represented by $y_{1} = 10 \sin (50 πt - 0 .252) mm y_{2} = 4 \cos (50 πt - 0 .25 x) mm$ and $y_{3} = 7 \sin (50 πt - 0 .25 x + π) mm$ arrive at a given point. Then the resultant wave is represented by

Difficult

A

$y = 5 \cos (50 πt - 0 .25 x + \frac{π}{4})$
B

$y = 3 \sin (50 πt - 0 .25 x + \frac{π}{3})$
C

$y = 5 \sin (50 πt - 0 .25 x + \tan^{- 1} \frac{4}{3})$
D

$y = 4 \cos (50 πt - 0 .25 x + \tan^{- 1} \frac{4}{3})$

Solution

$\begin{array}{l} y = y_{1} + y_{2} + y_{3} \\ = 10 \sin (50 πt - 0 .25 x) + 4 \cos (50 πt - 0 .25 x) + 7 \sin (50 πt - 0 .25 x + π) \end{array}$
$= 10 \sin (50 πt - 0 .25 x) - 7 \sin (50 πt - 0 .25 x) + 4 \cos (50 πt - 0 .25 x)$
$= 3 \sin (50 πt - 0 .25 x) + 4 \cos (50 πt - 0 .25 x)$
$\begin{array}{l} \Rightarrow y = \sqrt{3^{2} + 4^{2}} \sin (50 πt - 0 .25 x + \tan^{- 1} \frac{4}{3}) \\ \Rightarrow y = 5 \sin (50 πt - 0 .25 x + \tan^{- 1} \frac{4}{3}) mm \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App