Define constructive interference.

Two waves having equations $x_1=a\sin \left(\omega t+{\varphi }_1\right),$ $x_2=a\sin \left(\omega t+{\varphi }_2\right)$. If in the resultant wave the frequency and amplitude remain equal to those of superimposing waves. Then phase difference between them is

A loudspeaker $L$ is placed in the hall with two doors $D_1$ and $D_2$ as shown below. The distance between $D_1$ and $D_{\mathit{2}}$ is $8.5 \mathrm{m}$. The loudspeaker $L$ is equidistant from $D_{\mathit{1}}$ and $D_{\mathit{2}}$ Monotonic sound waves are emitted from the loudspeaker, and it is found that at point $P$ which is $6.0 \mathrm{m}$ from $D_{\mathit{1}}$ and at point $Q$ the sound intensities are minimum. The line joining $D_{\mathit{1}}\mathit{,}P$ and $Q$ is perpendicular to the line joining $D_{\mathit{1}}$ and $D_{\mathit{2}}$. No other minimum intensity locations can be found between $P \mathrm{and} Q$ and beyond $Q$ along the $PQ$ line. What is the frequency of the sound wave generated by the loudspeaker ?(Speed of sound is $340 \mathrm{m}/\mathrm{s}$ )

Four different independent waves are represented by

(i)  $y_1=a_1\sin \omega t$ 

(ii) $y_2=a_2\sin 2\omega t$

(iii) $y_3=a_3\sin \omega t$

(iv) $y_4=a_4\sin \left(\omega t+\frac{\pi }{3}\right)$

With which two waves, interference is possible?

The superposing waves are represented by the following equations

$y_1=5 \sin 2\mathrm{\pi }(10t-0.1x)$
$y_2=10 \sin 2\mathrm{\pi }(10t-0.1x)$

Then what would be the ratio of maximum to minimum intensity, $\frac{I_{\max }}{I_{\min }}$?

Out of the given four waves $\left(1\right), \left(2\right), \left(3\right)$ and $\left(4\right)$

$y=a\sin (kx+\omega t) ...\left(1\right)$                           

$y=a\sin (\omega t-kx) ...\left(2\right)$                           

$y=a\cos (kx+\omega t) ...\left(3\right)$                     

$y=a\cos (\omega t-kx) ...\left(4\right)$                      

emitted by four different sources $S_1, S_2, S_3$ and $S_4$ respectively, interference phenomena would be observed in space under appropriate conditions when