Question

Three waves of equal frequency having amplitudes $10mm,4mm$ and $7mm$ arrive at a given point with successive phase difference $\frac{\pi }{2}$. The amplitude of the resulting wave (in mm) is given by:

• A. $7$
• B. $6$
• C. $5$
• D. $4$

Answer 1

The correct option is C $5$

It is given that the $3$ waves arrive at a point with a successive difference of ${90}^o$.

Therefore, the waves with amplitude $10mm$ and $7mm$ will be completely out of phase and interfere destructively.

Hence, the amplitude of the resultant wave is $10-7=3mm$

Now, the waves of $3mm$ and $4mm$ are out of phase by ${90}^o$

Therefore, applying Pythagorus theorem, they will interfere with each other causing the new amplitude of the wave to be,

$A^2=3^2+4^2$

$A^2=25$ or $A=5mm$