Principle of Superposition of Waves

There is a destructive interference between the two waves of wavelength $\lambda$ coming from two different paths at a point. To get maximum sound or constructive interference at that point, the path of one wave is to be increased by 

Two plane progressive waves shows destructive interference at point$P$. Which of the following statement is true at point $P$:-
 

A body is suspended from a string of length $1 \mathrm{m}$ and mass $2 \mathrm{g}$. The mass of the body to produce a fundamental mode of $100 \mathrm{Hz}$ frequency in the string is
(Acceleration due to gravity $=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The equations of two waves are given by :

$y_1=5\sin 2\pi \left(x-vt\right) \mathrm{cm}$

$y_2=3\sin 2\pi \left(x-vt+1.5\right) \mathrm{cm}$

These waves are simultaneously passing through a string. The amplitude of the resulting wave is :

Equation of resultant wave on string after interference :-

(iii) Two waves ${\mathrm{y}}_1=8\sin \left(\mathrm{wt}-\frac{\mathrm{\pi }}{2}\right)$ and ${\mathrm{y}}_2=6\sin \left(\mathrm{wt}-\frac{\mathrm{\pi }}{2}\right)$ are interfering one another. What will be the resultant amplitude.

Equation of resultant wave on string after interference :-

Equation of resultant wave on string after interference :-

(i) The amplitude of two interfering waves are $2a \& 3a$ respectively. The resultant amplitude in case if consructive interference.

Three harmonic waves having equal frequency $v$ and same intensity $I_0$ , have phase angles $0,\frac{\pi }{4}$ and $-\frac{\pi }{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to:

A travelling wave represented by $y\left(x, t\right)=a sin\left(kx-\mathrm{\omega }t\right)$ is superimposed on another wave represented by $y\left(x, t\right)=\mathrm{a sin}\left(kx+\mathrm{\omega }t\right)$ . The resultant is a

A wave represented by the equation $y=a\cos \left(kx-\omega t\right)$ is superposed with another wave to form a stationary wave such that the point $x=0$ is a node. The equation of the other wave is,

An organ pipe open at both ends produces:

The maximum intensity of fringes in Young's experiment is $I$. If one of the slit is closed then, the intensity at that place becomes $I_o$. Which of the following relations is true? 

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

Two waves are passing through a region in the same direction at the same time. If the equation of these wave are

$y_1=a\sin \frac{2\pi }{\lambda }\left(vt-x\right)$

$y_2=b\sin \frac{2\pi }{\lambda }\left[\left(vt-x\right)+x_0\right]$,

then the amplitude of the resultant wave for $x_0=\frac{\lambda }{2}$ is,

Principle of superposition for displacement is valid for :-

Four sources of light waves are represented by :-
$\left(\mathrm{i}\right) y=a_1\sin \left(3\omega t\right)$
$\left(\mathrm{ii}\right) y=a_2\sin \left(\omega t+\varphi \right)$
$\left(\mathrm{iii}\right) y=a_1\sin \left(2\omega t\right)$
$\left(\mathrm{iv}\right) y=a_2 \sin \left[2\left(\omega t+\varphi \right)\right]$
Interference fringes may be observed due to superposition of:

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 $340 \mathrm{m}/\mathrm{s}$ )

What combination of the following transverse waves will represent a wave travelling along a direction making an angle $45°$ with the positive $x$ and $y$ axes

$z_1=A\cos (kx-\omega t)$

$z_2=A\cos (kx+\omega t)$

$z_3=A\cos (ky-\omega t)$

Figure shows a Young’s double slit experiment setup. The source $S$ of wavelength $4000Å$ oscillates along $y-$ axis according to the equation $y=\sin \pi t$, where $y$ is in millimeters and $t$ is in seconds. The distance between two slits $S_1$ and $S_2$ is $0.5\mathrm{m}\mathrm{m}$.

If the phase difference between two waves of the same frequency is $2\mathrm{\pi }$ during superposition, then the resultant amplitude is