What is a destructive interference?

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

Two pulses travel in mutually opposite directions in a string with a speed of $2.5 \mathrm{cm}/\mathrm{s}$ as shown in the figure. Initially the pulses are $10 \mathrm{cm}$ apart. What will be the state of the string after two seconds? 

Two waves of same frequency have amplitudes $5 \mathrm{cm} \text{and} 3 \mathrm{cm}$. These waves are made to superpose in the same direction. The ratio of maximum intensity to minimum intensity at various places will be

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?

When interference is produced by two progressive waves of equal frequencies, then the maximum intensity of the resulting sound are $N$ times the intensity of each of the component waves. The value of $N$ 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 $340 \mathrm{m}/\mathrm{s}$ )

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