Question

Waves from two sources superpose on each other at a particular point amplitude and frequency of both the waves are equal. The ratio of intensities when both waves reach in the same phase and they reach with the phase difference of ${90}^{\circ }$ will be

• A. $1:1$
• B. $\sqrt{2}:1$
• C. $2:1$
• D. $4:1$

Answer 1

The correct option is C $2:1$

Relation between intensity $f$

Amplitude

$I=k{A}^2{\cos }^2\left(\frac{|theta}{2}\right)$

When both the waves reach in the same phase, then

$\theta =0^o$

$I_1=k{A}^2{\cos }^2\left(\frac{0^o}{2}\right)$

$I_1=k{A}^2[\cos 0^o=1]$ ------- $\left(1\right)$

When both the waves reach with phase difference ${90}^o$.

$\theta ={90}^o$

$I_2=k{A}^2{\cos }^2\left(\frac{{90}^o}{2}\right)$

$I_2=k{A}^2{\cos }^2\left({45}^o\right)$

$I_2=k{A}^2\left(\frac{1}{2}\right)$ ----- $\left(2\right)$

$\frac{I_1}{I_2}=\frac{k{A}^2}{k{A}^2\left(1/2\right)}=\frac{2}{1}$