Resultant Amplitude

Q.

Two waves represented by $y$ = $asin(wt-kx)$ and $y$ = $acos(wt-kx)$ are superposed. The resultant wave will have an amplitude

1. a

2. $\sqrt{2}a$

3. 2a

4. 0

Q. Two waves, $y_1=2a\cos \omega t$ and $y_2=3a\cos (\omega t+\frac{\pi }{2})$ meet at a point. The amplitude of the resultant wave is

1. $a$
2. $5a$
3. $3.6a$
4. $2.5a$

Q.

Name the factors in Doppler effect on which the change in frequency depends.

Q. Two waves are passing simultaneously through a string.
The equation of the waves are given by,
$y_1=A_1\sin k(x-vt)$
and $y_2=A_2\sin k(x-vt+x_0)$
Where the wave number $k=6.28{\text{cm}}^{-1}$ and $x_0=1.50\text{cm}$ The amplitudes are $A_1=5.0\text{mm}$ and $A_2=4.0\text{mm}$. Find the phase difference between the waves and the amplitude of the resulting wave.

1. $2\pi \text{and}1\text{mm}$
2. $3\pi \text{and}1\text{mm}$
3. $\pi \text{and}2\text{mm}$
4. $\pi \text{and}0.5\text{mm}$

Q. Two waves represented by equation $y_1=A\sin (\omega t-kx+{\varphi }_1)$ and $y_2=A\sin (\omega t-kx+{\varphi }_2)$ are superimposed such that the amplitude of resultant wave is $A$. Find the phase difference between them.
Given: $({\varphi }_1>{\varphi }_2)$

1. ${90}^{\circ }$
2. ${120}^{\circ }$
3. ${60}^{\circ }$
4. ${135}^{\circ }$

Q. Two identical travelling waves, moving in the same direction, are out of phase by $\frac{\pi }{2}\text{rad}$. If amplitude of each wave is $A$, then find the resultant amplitude of the wave after superimposition.

1. $1.41A$
2. $2.16A$
3. $1.6A$
4. $6A$

Q. Two sinusoidal waves each of amplitude $2A$, travel in the same direction in a medium. If the phase difference between the two waves is ${120}^{\circ }$, then find the resultant amplitude of the superimposed wave.

1. $3\sqrt{2}A$
2. $2A$
3. $\sqrt{2}A$
4. $3A$

Q.

Two waves passing through a region are represented by

$y=1.0cmsin\left[\right(3.14c{m}^{-1})x-(157s^{-1}\left)t\right]$

and $y=1.5cmsin\left[\right(1.57c{m}^{-1})x-(314s^{-1}\left)t\right]$

Find the displacement of the particle at x = 4.5 cm at time t = 5.0 ms.

1. 0.35 cm

2. $\left(\frac{1}{\sqrt{2}}\right)$cm

3. $\left(\frac{1.5}{\sqrt{2}}\right)$cm

4. - 0.35 cm

Q. A wave is represented by $y_1=10\cos (5x+25t)$, where $x$ and $y$ are measured in $\text{centimetres}$ and $t$ in $\text{seconds}$. A second wave for which
$y_2=20\cos (5x+25t+\pi /3)$ interferes with the first wave. Find the amplitude and phase of the resultant wave.

1. $26.46\text{cm},0.71\text{rad}$
2. $28.50\text{cm},1\text{rad}$
3. $30\text{cm},0.71\text{rad}$
4. $30.46\text{cm},0.6\text{rad}$

Q. Two sources of sound $\text{A}$ and $\text{B}$ produce waves of $350\text{Hz}$. The particle at point $\text{P}$ is vibrating under the influence of these two waves. The amplitudes of the two waves are $0.3\text{mm}$ and $0.4\text{mm}$. If $AP-BP=25\text{cm}$ and velocity of sound is $350\text{m/s}$, the resultant amplitude of the particle at point $\text{P}$ will be

1. $0.7\text{mm}$
2. $0.1\text{mm}$
3. $0.2\text{mm}$
4. $0.5\text{mm}$

Q. Two wave with same frequency and wave number are propagating in the same direction. The ratio of their amplitude is $5:1$ . If interference occurs, the ratio of maximum and minimum intensity should be

1. $9:4$
2. $3:2$
3. $1:4$
4. $4:1$

Q. Two wave with same frequency and wave number are propagating in the same direction. The ratio of their amplitude is $5:1$ . If interference occurs, the ratio of maximum and minimum intensity should be

1. $9:4$
2. $3:2$
3. $1:4$
4. $4:1$

Q. On the superposition of the two waves represented by equation,
$y_1=A\sin (\omega t-kx)$
$y_2=A\cos (\omega t-kx+\frac{\pi }{6})$
The resultant angular frequency of the oscillation will be

1. $\omega$
2. $2\omega$
3. $\frac{\omega }{2}$
4. $3\omega$

Q. Two waves $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\varphi )$ are superimposed such that the resultant amplitude of oscillation is $\sqrt{2}A$, then the value of $\varphi$ is

1. $\frac{\pi }{2}$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{3}$
4. $\frac{\pi }{6}$

Q. Two waves of equal amplitude A, and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is

1. \N
2. A
3. 2A
4. between 0 and 2A

Q. Two waves are passing through a region in the same direction at the same time. If the equation of these waves are
$y_1=\alpha \sin \frac{2\pi }{\lambda }(vt-x)$
and $y_2=\beta \sin \frac{2\pi }{\lambda }\left[\right(vt-x)+\varphi ]$,
then the amplitude of the resultant wave for $\varphi =\frac{\lambda }{2}$ is

1. $|\alpha -\beta |$
2. $\alpha +\beta$
3. $\sqrt{{\alpha }^2+{\beta }^2}$
4. $\sqrt{{\alpha }^2+{\beta }^2+2\alpha \beta cosx}$

Q. Two sinusoidal waves each of amplitude $2A$, travel in the same direction in a medium. If the phase difference between the two waves is ${120}^{\circ }$, then find the resultant amplitude of the superimposed wave.

1. $3\sqrt{2}A$
2. $2A$
3. $\sqrt{2}A$
4. $3A$

Q. Three components of sinusoidal progressive waves travelling in the same direction along the same path having the same period, but with amplitudes $A,A/2$ and $A/3$. The phase of the vibration at any position $x$ on their path at time $t=0$ are $0,-\pi /2$ and $\pi$ respectively. Find the amplitude and phase of the resultant wave

1. $\frac{5A}{6},{\tan }^{-1}\left(3/4\right)$
2. $\frac{5A}{2},{\tan }^{-1}\left(4/3\right)$
3. $\frac{6A}{5},{\tan }^{-1}\left(2/3\right)$
4. $\frac{5A}{6},{\tan }^{-1}\left(4/3\right)$

Q. Two monochromatic sinusoidal waves, each of intensity $I$, have a constant phase difference of $\varphi$. These waves when superimposed, form a resultant sinusoidal wave. Then, the intensity of the resultant wave is

1. $4I$
2. $4I\cos \varphi$
3. $4I{\cos }^2\varphi$
4. $4I{\cos }^2\left(\frac{\varphi }{2}\right)$

Q. Two waves of equal amplitudes and wavelengths but differing in phase are superimposed. Amplitude of resultant wave is maximum when phase difference is

Q. Two waves of equal amplitude $\left(A\right)$, frequency $\left(f\right)$ and intensity $\left(I\right)$ propagate along the same direction in a medium. The intensity of resultant wave will be:

1. $0$
2. $2I$
3. $4I$
4. Between $0\text{and}4I$

Q. Two waves $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\varphi )$ are superimposed such that the resultant amplitude of oscillation is $\sqrt{2}A$, then the value of $\varphi$ is

1. $\frac{\pi }{2}$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{3}$
4. $\frac{\pi }{6}$

Q. On the superposition of the two waves represented by equation,
$y_1=A\sin (\omega t-kx)$
$y_2=A\cos (\omega t-kx+\frac{\pi }{6})$
The resultant angular frequency of the oscillation will be

1. $\omega$
2. $2\omega$
3. $\frac{\omega }{2}$
4. $3\omega$

Q. Two sinusoidal waves produced by two vibrating sources $A$ and $B$ of equal frequencies, are propagating to the point $P$ along a straight line. The amplitude of both of the waves at $P$ is ${}^{\prime }{a}^{\prime }$ and the initial phase of $A$ is ahead by $\frac{\pi }{3}$ than that of $B$. The distance $AP$ is greater than $BP$ by $50\text{cm}$. If the wavelength is $1\text{m},$ then the resultant amplitude at the point $P$ will be

1. $2a$
2. $a\sqrt{3}$
3. $a\sqrt{2}$
4. $a$

Q. Two waves of equal amplitude $\left(A\right)$, frequency $\left(f\right)$ and intensity $\left(I\right)$ propagate along the same direction in a medium. The intensity of resultant wave will be:

1. $0$
2. $2I$
3. $4I$
4. Between $0\text{and}4I$

Q. Two waves represented by equation $y_1=A\sin (\omega t-kx+{\varphi }_1)$ and $y_2=A\sin (\omega t-kx+{\varphi }_2)$ are superimposed such that the amplitude of resultant wave is $A$. Find the phase difference between them.
Given: $({\varphi }_1>{\varphi }_2)$

1. ${90}^{\circ }$
2. ${120}^{\circ }$
3. ${60}^{\circ }$
4. ${135}^{\circ }$

Q. On the superposition of the two waves represented by equation $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\frac{\pi }{4})$, the resultant amplitude of oscillation will be:

1. $A\sqrt{2}$
2. $A\sqrt{2+\sqrt{2}}$
3. $A\sqrt{2+\sqrt{3}}$
4. $A\sqrt{1+\sqrt{2}}$

Q. On the superposition of the two waves represented by equation,
$y_1=A\sin (\omega t-kx)$
$y_2=A\cos (\omega t-kx+\frac{\pi }{6})$
The resultant angular frequency of the oscillation will be

1. $\omega$
2. $2\omega$
3. $\frac{\omega }{2}$
4. $3\omega$

Q. Two waves of equal frequencies have their amplitudes in the ratio of $3:5$. They are superimposed on each other. The ratio of maximum and minimum intensities of the resultant wave is