Superposition of Waves

Two light beams of intensities in the ratio of $9:4$ are allowed to interfere. The ratio of the intensity of maxima and minima will be :

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

When two progressive waves $y_1=4\sin (2x-6t)$ and $y_2=5\sin \left(2x-6t-\frac{\pi }{2}\right)$ are superimposed, the amplitude of the resultant wave is $\sqrt{x} \mathrm{unit}$.  Find the value of $x$.

Two identical sources of sound $S_1$ and $S_2$ produce intensity $I_0$ at a point $P$ equi distant from source. If power of $S_1$ is reduced to $64\%$ and phase difference between two sources is varied then let $I_{max}$ is maximum intensity at point $P$. Find $100\times \frac{I_{max}}{I_0}.$

Two speakers connected to the same source of fixed frequency are placed $2 \mathrm{m}$ apart in a box. A sensitive microphone placed at a distance of $4 \mathrm{m}$ from their midpoint along the perpendicular bisector shows a maximum response. The box is slowly rotated until the speakers are in line with the microphone. The distance between the midpoint of the speakers and the microphone remains the same. Exactly five maximum responses are observed in the microphone in doing this. The wavelength of sound wave is (in $\mathrm{m}$):

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 disturbances produced by two sound sources cannot be cancelled as the disturbance by each wave is added.

What do you understand by principle of superposition of waves?

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,

Two loudspeakers $L_1$ and $L_2$ driven by a common oscillator and amplifier, are arranged as shown. The frequency of the oscillator is gradually increased from Zero and the detector at D records a series of maxima and minima.If the speed of sound is $330 {\mathrm{ms}}^{-1}$ then the frequency at which the first maximum is observed is:

The amplitude of a wave represented by displacement equation $\mathrm{y}=\frac{1}{\sqrt{\mathrm{a}}}\sin \mathrm{\omega t}\pm \frac{1}{\sqrt{\mathrm{b}}}$ $\mathrm{cos\omega t}$ will be

Two loudspeakers $1.0 \mathrm{m}$ apart are coherent sources which emit sound waves of wavelength $1.0 \mathrm{m}$. A microphone moving along OP records the first minimum at $\mathrm{P}$. If ${\mathrm{L}}_2\mathrm{P}$ is $4 \mathrm{m}, {\mathrm{L}}_1\mathrm{P}$ is equal to :

Principle of superposition for displacement is valid for :-