Resultant Amplitude

Q. $y(x,t)=\frac{0.8}{\left[\right(4x+5t{)}^2+5]}$ represents a moving pulse where $x$ and $y$ are in metre and $t$ in second. Then

1. Pulse is moving in positive $x-$direction.
2. In $2$ second, it will travel a distance of $2.5m$
3. Its maximum displacement is $0.16m$
4. It is a symmetric pulse

Q.

The ratio of intensities of two waves is given by 4:1.The ratio of the amplitude of the waves is:

1. 1:2

2. 4:1

3. 1:4

4. 2:1

Q.

A source of sound operates at 2.0 kHz, 20 W emitting sound uniformly in all directions. The speed of sound in air is 340 m s and the density of air is $1.2kg{m}^{-3}$. (a) What is the intensity at a distance of 6.0 m from the source ? (b) What will be the pressure amplitude at this point ? (c) What will be the displacement amplitude at this point ?

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

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. 2A

2. between 0 and 2A

3. 0

4. A

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. 0.35 cm

3. 

4. 

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

Q. 62. In ydse if intensity ratio of bright and dark fringes is 81:25 . The ratio intensity of two waves is ??

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 at the point $\text{P}$ produced by 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. $0.2\text{mm}$
3. $0.5\text{mm}$
4. $0.1\text{mm}$

Q.

The displacement vs time graph for two waves A and B which travel along the same string are shown in the figure. Their intensity ratio $\frac{I_A}{I_B}$ is

1. 

2. 

3. 

4. 

Q. Three components of sinusoidal progressive waves travelling in the same direction along the same path having the same period, but with amplitudes are $A,A/2$ and $A/3$. The phase of the variation 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. $\frac{5A}{2},{\tan }^{-1}\left(4/3\right)$
2. $\frac{5A}{6},{\tan }^{-1}\left(4/3\right)$
3. $\frac{5A}{6},{\tan }^{-1}\left(3/4\right)$
4. $\frac{6A}{5},{\tan }^{-1}\left(2/3\right)$

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 $y_1=A\sin (\omega t-kx)$ 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 $y_1=A\sin (\omega t-kx)$ and $y_2=A\sin (\omega t-kx+\frac{\pi }{4})$, the resultant amplitude of oscillation will be:

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

Q. In the YDSE, the point source is placed slightly off the central axis, as shown in the figure. Find the nature & order of the interference at point $\text{P}$ ($\lambda =500\text{nm}$).

1. Maxima, $70$
2. Minima, $120$
3. Maxima, $120$
4. Minima, $70$

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

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. $30.46\text{cm},0.6\text{rad}$
4. $30\text{cm},0.71\text{rad}$

Q. Ratio of intensities of two light waves is given by 4 : 1. The ratio of the amplitudes of the waves is:

1. 2 : 1
2. 1 : 2
3. 4 : 1
4. 1 : 4

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 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 every wave at $P$ is ${}^{\prime }{a}^{\prime }$ and the 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. $a\sqrt{2}$
3. $a$
4. $a\sqrt{3}$

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 waves each having a frequency of 100 Hz and a wavelength of 2 cm are travelling in the same direction on a string. Both the waves were produced at the same instant but the first one was produced at a distance 4 cm behind the second one. If both waves have an amplitude of 2 mm what would be the amplitude of the resultant wave?

1. 2 mm

2. 0 mm

3. 3 mm

4. 4 mm

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. In the setup shown in the figure $(D>>d)$ and $d=4\lambda$. Find the total number of maxima on the screen.

1. $5$
2. $6$
3. $7$
4. $8$

Q. On the superposition of the two waves given as $y_1=A_0\sin (\omega t-kx)$ and $y_2=A_0\cos (\omega t-kx+\frac{\pi }{6})$ the resultant amplitude of oscillation will be

1. $\frac{A_0}{2}$
2. $A_0$
3. $\sqrt{3}{A}_0$
4. $\frac{3}{2}{A}_0$

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. 2a

3. $\sqrt{2}a$

4. 0

Q. The amplitudes of two interfering waves are $4cm$ and $3cm$ respectively. If the resultant amplitude is $1cm$ then the interference becomes

1. constructive
2. Destructive
3. Both constructive and destructive
4. given data is insufficient

Q. Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120${}^{\circ }$. The resultant amplitude will be

1. 4A

2. A

3. 2A

4.