Variation of Intensity in Space

Q.

Two coherent narrow slits emitting sound of wavelength $\lambda$ in the same phase are placed parallel to each other at a small separation of $2\lambda$. The sound is detected by moving a detector on the screen E at a distance $D(>>\lambda )$ from the slit S, as shown in figure (16-E6). Find the distance x such that the intensity at P is equal to the intensity at O.

Q. Two coherent sources of sound, $S_1$ and $S_2$, produce sound waves of the same wavelength $\lambda =1\text{m}$, in phase. $S_1$ and $S_2$ are placed $1.5\text{m}$ apart (see fig.). A listener, located at $L$, directly in front of $S_2$ finds that the intensity is a minimum where he is $2\text{m}$ away $S_2$. The listener moves away from $S_1$, keeping his distance from $S_2$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance $d$ from $S_1$. Then $d$ is

1. $\text{12 m}$
2. $\text{5 m}$
3. $\text{2 m}$
4. $\text{3 m}$

Q. Two towers on top of two hills are $40\text{km}$ apart. The line joining them passes $50\text{m}$ above a hill halfway between the towers. What is the longest wavelength of radio waves, which can be sent between the towers without appreciable diffraction effects?

Q. The intensity of a sound wave gets reduced by 20% on passing through a slab. The reduction in intensity on passage through two such consecutive slabs is

1. 50%
2. 30%
3. 40%
4. 36%

Q. Sound waves of wavelength $\lambda$ travelling in a medium with a speed of $vm/s$ enter into another medium where its speed is $2vm/s$. Wavelength of sound waves in the second medium is

1. $\lambda$
2. $2\lambda$
3. $4\lambda$
4. $\lambda /2$

Q. Figure shows two coherent sources $S_1$ and $S_2$ which emit sound of wavelength $\lambda$ in phase. The separation between the source is $3\lambda$. A circular wire of large radius is placed in such a way that $S_1{S}_2$ lies in its plane and the midpoint of $S_1{S}_2$ is at the centre of the wire. Find the number of angular positions $\theta (\theta <{90}^{\circ })$ on the wire for which constructive interference takes place.

Q. A small source of sound moves on a circle as shown in the figure and an observer is standing on $O$. Let $n_1$, $n_2$ and $n_3$ be the frequencies heard when the source is at $A,B$ and $C$ respectively. Then

1. $n_1>n_2>n_3$
2. $n_2>n_1>n_3$
3. $n_1=n_2>n_3$
4. $n_2>n_3>n_1$

Q. An $EM$ wave radiates outwards from a dipole antenna, with $E_o$ as the amplitude of its electric field vector. The electric field $E_o$ which transports significant energy from the source falls off as:

1. Remains constant
2. $\frac{1}{r^3}$
3. $\frac{1}{r}$
4. $\frac{1}{r^2}$

Q. Two interfering waves have intensities in the ratio $9:1$. Then the ratio of maximum to maximum intensity is:

1. $16:4$
2. $4:2$
3. $100:64$
4. $10:8$

Q. Two waves in the same medium are represented by $y-t$ curves in the figure. Find the ratio of their average intensities.

1. $\frac{4}{5}$
2. $\frac{5}{4}$
3. $\frac{25}{16}$
4. $\frac{16}{25}$

Q. An observer approaches towards a stationary source of sound at constant velocity and recedes away at the same speed. The graph of wavelength observed with time is:

1. 
2. 
3. 
4. 

Q. Sound waves of frequency $320Hz$ are sent into the top of a vertical tube containing water at a level that can be adjusted. Standing waves are produced at two successive water levels $44cm$ and $74cm$ from open end. The distance (in $cm$) of nearest displacement antinode from open end is

Q.

Two cars $\mathrm{A}$ and $\mathrm{B}$ are moving away from each other in opposite directions. Both the cars are moving at a speed of $20\mathrm{m}/\mathrm{s}$ with respect to the ground. If an observer in car $\mathrm{A}$ detects a frequency of $2000\mathrm{Hz}$ of the sound coming from car $\mathrm{B}$, what is the natural frequency of the sound source in car $\mathrm{B}$? (speed of sound in air $=340\mathrm{m}/\mathrm{s}$)

1. $2250\mathrm{Hz}$

2. $200\mathrm{Hz}$

3. $2300\mathrm{Hz}$

4. $2150\mathrm{Hz}$

Q. The faintest sound that can be heard has a pressure amplitude of about $4\times {10}^{-5}{\text{N/m}}^2$ and the loudest that can be heard without pain has a pressure amplitude of about $2.8{\text{N/m}}^2$. Determine the intensity of the faintest sound (both in ${\text{W/m}}^2$ and in $\text{dB}$).
[Assume, air density is $1.3{\text{kg/m}}^3$ and velocity of sound is $330\text{m/s}$ and take ${\log }_{10}1.86=0.269$]

1. $2\times {10}^{-12}{\text{W/m}}^2,1\text{dB}$
2. $1.86\times {10}^{-12}{\text{W/m}}^2,1.6\text{dB}$
3. $1.86\times {10}^{-12}{\text{W/m}}^2,2.7\text{dB}$
4. $2\times {10}^{-12}{\text{W/m}}^2,2.7\text{dB}$

Q. The velocity of electromagnetic waves in a dielectric medium $({\epsilon }_r=4)$ is

1. $7.5\times {10}^7$ meter /second
2. $6\times {10}^8$ meter /second
3. $1.5\times {10}^8$ meter /second
4. $3\times {10}^8$ meter /second

Q. Sound waves are emitted uniformly in all directions from a point source. The dependence of sound level $\beta$ in decibels on the distance $r$ can be expressed as ($a$ and $b$ are positive constants)

1. $\beta =a-\frac{b}{r^2}$
2. $\beta =a-b(logr{)}^2$
3. $\beta =a-blogr$
4. $\beta =-blog{r}^2$

Q. When a person wears a hearing aid, the sound intensity level increases by 30 dB. The sound intensity increases by

1. 
2. 
3. 
4. 

Q. A and B are two wave trains shown in the figure, the ratio of intensity of A to B is

1. $1$
2. $2$
3. $4$
4. $8$

Q. A long string of mass per unit length 0.2 Kg/m is stretched to a tension 500 N. A transverse wave of amplitude A = 10 mm and $\lambda$ = 0.5 m is travelling on this string. This string is joined to another string of same cross section and mass per unit length $0.8$ kg/m. The fraction of the average power carried by the wave in the first string that is transmitted to the second string is K/9. Find K.

Q. Two coherent point sources $S_1$ and $S_2$ vibrating in phase emit light of wavelength $\lambda$. The separation between the sources is $2\lambda$. Consider a line passing through $S_2$ and perpendicular to the line $S_1{S}_2$. Find the position of farthest minima.

1. $D=\frac{\lambda }{2}$
   
2. $D=\frac{15\lambda }{12}$
   
3. $D=\frac{15\lambda }{4}$
   
4. $D=\frac{\lambda }{3}$
   

Q.

A sound made on the surface of a lake takes $3s$ to reach a boatman. How much time will it take to reach a diver inside the water at the same depth?

Velocity of sound in air $=330m{s}^{-1}$

Velocity of sound in water $=1450$

Q. An electromagnetic wave of frequency $1\times {10}^{14}$ Hertz is propagating along z-axis. The amplitude of electric field is $4V/m$. If ${\in }_0=8.8\times {10}^{-12}{C}^2/N-m^2$, then average energy density of electric field will be:

1. $35.2\times {10}^{-12}J/m^3$
2. $35.2\times {10}^{-11}J/m^3$
3. $35.2\times {10}^{-10}J/m^3$
4. $35.2\times {10}^{-13}J/m^3$

Q. Light of intensity ${10}^{–5}W{/}^2$ falls mon a sodium photocell of surface area $2{\text{cm}}^2$ . Assuming that the top 5 layers of sodium absorb the incident energy, estimate time required for photoelectric emission in the wave-picture of radiation. The work function for the metal is given to be about $2eV$. What is the implication of your answer?

Q.

Number of waves of orange light emitted by krypton in 1 m is ____________.

Q. In the figure below, $P$ and $Q$ are two equally intense coherent sources emitting radiation of wavelength $20\text{m}$. The separation between $P$ and $Q$ is $5\text{m}$ and the phase of $P$ is ahead of that of $Q$ by ${90}^{\circ }.A,B$ and $C$ are three distinct points of observation, each equidistant from the midpoint of $PQ.$ The intensities of radiation at $A,B,C$ will be in the proportion,

1. $0:1:4$
2. $2:1:0$
3. $0:1:2$
4. $4:1:0$

Q. A person is standing at a distance $D$ from an isotropic point source of sound. He walks $50.0m$ towards the source and observes that the intensity of the sound has doubled. His initial distance $D$ from the source is

1. $\frac{50}{\sqrt{2}-1}m$
   
2. $50\sqrt{2}m$
   
3. $100\sqrt{2}m$
   
4. $\frac{50\sqrt{2}}{\sqrt{2}-1}m$
   

Q. Sinusoidal waves 5.00 cm in amplitude are to be transmitted along a string having a linear mass density equal to $4.00\times {10}^{-2}kg/m$. If the source can deliver a maximum power of 90 W and the string is under a tension of 100 N, then the highest frequency at which the source can operate it, is $(take{\pi }^2=10)$

1. 62.3 Hz
2. 30 Hz
3. 45.3 Hz
4. 50 Hz

Q. The same progressive wave is represented by two graphs $I$ and $II$. Graph $l$ shows how the displacement $y$ varies with the distance $x$ along the wave at a given time. Graph $II$ shows how $y$ varies with time $t$ at a given point on the wave. The ratio of measurements $AB$ to $CD,$ marked on the curves, represents

1. wave number $k$
2. frequency $v$
3. wave speed $V$
4. angular frequency $\omega$

Q. A transverse wave is propagating along $+x$ direction. At $t=2s,$ the particle at $x=4m$ is at $y=2mm.$ With the passage of time, its $y$ coordinate increases and reaches to a maximum of $4mm.$ The wave equation is (Using $\omega$ and $k$ with their usual meanings)

1. $y=4\sin \left[\omega \right(t-2)-k(x-4)+\frac{\pi }{6}]$
2. $y=4\sin \left[\omega \right(t+2)+k(x)+\frac{\pi }{6}]$
3. $y=4\sin \left[\omega \right(t-2)-k(x-4)+\frac{5\pi }{6}]$
4. $y=4\sin \left[\omega \right(t+2)+k(x-2)+\frac{\pi }{6}]$

Q. Change in temperature of the medium changes