Need for Intensity

Q. A uniform thin rope of length $12\text{m}$ and mass $6\text{kg}$ hangs vertically from a rigid support and a block of mass $2\text{kg}$ is attached to its free end. A transverse short wave-train of wavelength $6\text{cm}$ is produced at the lower end of the rope. What is the wavelength of the wave train (in$\text{cm}$) when it reaches the top of the rope?

1. $3$
2. $6$
3. $12$
4. $9$

Q. What are the conditions for maxima and minima in case of Young's double slit experiment?

Q.

The ratio of the amplitude of two waves is $4:9$. What is the ratio of their intensities?

Q. A transverse wave $y=5\sin (3t-x)$, where $y,x,t$ are in SI units, is propagating on a stretched string having density $\rho =1{\text{kg/m}}^3$. Find the intensity of the propagating wave.

1. $200{\text{W/m}}^2$
2. $300{\text{W/m}}^2$
3. $325{\text{W/m}}^2$
4. $337.5{\text{W/m}}^2$

Q. A uniform rope of length $12\text{m}$ and mass $6\text{kg}$ hangs vertically from a rigid support. A block of mass $2\text{kg}$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06\text{m}$ is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope ?

1. $0.06\text{m}$
2. $0.12\text{m}$
3. $0.09\text{m}$
4. None of these

Q.

What is meant by the terms:
(a) amplitude
(b) frequency of a wave

Q. A uniform rope of length $12m$ and mass $6kg$ hangs vertically from a rigid support. A block of mass $2kg$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06m$ is produced at the lower end of the rope. What is the wavelength of the pulse when it reaches the top of the rope?

1. $0.06m$
2. $0.03$
3. $0.12m$
4. $0.09m$

Q. Assertion :Ratio of maximum intensity and minimum intensity in interference is 25 : 1. Hence amplitude ratio of two waves should be 3 : 2. Reason: $\frac{I_{max}}{I_{min}}={\left(\frac{A_1+A_2}{A_1-A_2}\right)}^2$

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Assertion is incorrect but Reason is correct

Q. The wave and particle nature of moving bodies can be observed at -

1. the same time.
2. the different time.
3. both options $\left(A\right)$ and $\left(B\right)$ are possible.
4. None of these

Q. For a wave displacement amplitude is ${10}^{-8}m$, density for air $1.3kg.m^{-3}$, velocity in air $340m^{-1}$ and frequency is $2000Hz$. The average intensity of wave is

1. $5.3\times {10}^{-4}W{m}^{-2}$
2. $5.3\times {10}^{-5}W{m}^{-2}$
3. $5.3\times {10}^{-8}W{m}^{-2}$
4. $5.3\times {10}^{-6}W{m}^{-2}$

Q. The ratio of intensities of two waves is $1:16$. The ratio of their amplitudes is

1. $16/17$
2. $1/4$
3. $1/16$
4. $1/2$

Q. The ratio of intensities of two sound waves is $4:9$. The ratio of their amplitudes will

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

Q. Sound waves of frequency $13.6\text{kHz}$ are emitted by two small coherent sources of sound placed d=1 m apart as shown at the centre of a circular toy train track. A person riding the train observes 4 maxima/sec when the train is running at a speed of $72\text{km/hr}$. The radius of the track is $\frac{100k}{\pi }m$. Find k. (velocity of sound in air is $340\frac{m}{s})$

Q. A particle of mass $10g$ is placed in potential field, given by $V=(50x^2+100)erg/g$. What will be frequency of oscillation of particle?

Q. Four harmonic waves of equal frequencies and equal intensities I${}_0$ have phase angles 0, $\pi$/3, 2$\pi$/3, and $\pi$. When they are superposed, the intensity of the resulting wave is nI${}_0$. The value of n is

Q. The equation of the transverse wave travelling in a rope is given by $y=5\sin (4t-0.02x)$ where $y$ and $x$ are in meters and $t$ is in seconds. Calculate the intensity of the wave if the density of rope material is $1250kg/m^3$

1. $2000kJ{m}^{-2}{s}^{-1}$
2. $10kJ{m}^{-2}{s}^{-1}$
3. $40kJ{m}^{-2}{s}^{-1}$
4. $3kJ{m}^{-2}{s}^{-1}$

Q. The path difference between two interfering waves of equal intensities at a point on the screen is $\frac{\lambda }{4}$. The ratio of intensity at this point and that at the central fringe will be

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

Q. In a stationary wave that from as a result of reflection of waves from an obstacle, the ratio of the amplitude at an antinode to the amplitude at node is 6. What percentage of energy is transmitted?

Q. Two sources A and B are producing notes of frequency 680 Hz. A detector moves from A to B with a constant velocity 2 m/s. Find number of beats heard by the detector per second, if velocity of sound v is 340 m/s.

Q. Two coherent sources have intensities in the ratio $25:16$. Find the ratio of intensities of maxima to minima?

Q. Two radio stations broadcast their programmes at the same amplitude $A$ and at slightly different frequencies ${\omega }_1$ and ${\omega }_2$ respectively where ${\omega }_1-{\omega }_2=1kHz$. A detector receives the signals from the two stations simultaneously. It can only detect signals of intensity $>2A^2.$ Find the interval between successive maxima of the intensity of the signal received by the detector.

1. $2\times {10}^{-3}s$
2. $1.5\times {10}^{-3}s$
3. ${10}^{-3}s$
4. $4\times {10}^{-3}s$

Q. The intensity of a wave is the amount of energy incident on a surface per sec

1. True
2. False

Q. A line source emits a cylindrical expanding wave. If the medium absorbs no energy then the amplitude will vary with distance $r$ from the source as proportional to

1. $r^{-1}$
2. $r^{-2}$
3. $r^{1/2}$
4. $r^{-1/2}$

Q. Equation of a progressive wave is given by $y=a\sin \pi [\frac{t}{2}-\frac{x}{4}]$, where t is in seconds and x is in meters. The distance through which the wave moves in 8 sec is ( in meter)

1. 8
2. 2
3. 16
4. 4

Q. As wave travels, intensity

1. increases
2. remains same
3. decreases
4. becomes negative

Q. At a certain instant a stationary transverse wave is found to have maximum kinetic energy. The appearance of string at that instant is

1. Straight line
2. Sinusoidal shape with amplitude $A/3$
3. Sinusoidal shape with amplitude $A/2$
4. Sinusoidal shape with amplitude $A$

Q. As a wave propagates,

1. the wave intensity decreases as the inverse of the distance from the source for a spherical wave
2. the wave intensity decreases as the inverse square of the distance form the source for a spherical wave
3. the wave intensity remains constant for a planewave
4. the wave intensity decreases as the inverse of the distance for a line source

Q. Two waves of same frequency but of amplitudes $a$ and $2a$ respectively superimpose over each other. The intensity at a point where the phase difference is $3\pi /2$, will be

1. $a$
2. $3a^2$
3. $5a^2$
4. $9a^2$

Q. A transverse wave is travelling along a string from left to right. The adjoining figure represents the shape of the string at a given instant. At this instant, among the following, choose the wrong statement:

1. Point A, B and H have downward velocity
2. Point C and G have zero velocity
3. Point A and E have minimum velocity
4. Point D, E and F have upward velocity.

Q. Which wave will have larger energy :

1. High frequency
2. Large amplitude
3. Both A and B
4. None of the above