Amplitude

Q.

In an electromagnetic wave, the direction of propagation is in the direction of

1. $\mathrm{E}$

2. $\mathrm{B}$

3. $\mathrm{E}\times \mathrm{B}$

4. None of these

Q. The magnetic field of a plane electromagnetic wave is

$\overrightarrow{B}=3\times {10}^{-8}\sin \left[200\pi \right(y+ct\left)\right]\hat{i}\text{T}$
Where $c=3\times {10}^8{\text{ms}}^{-1}$ is the speed of light.
The corresponding electric field is-

1. $\overrightarrow{E}=9\sin \left[200\pi \right(y+ct\left)\right]\hat{k}\text{V/m}$
2. $\overrightarrow{E}=-{10}^{-6}\sin \left[200\pi \right(y+ct\left)\right]\hat{k}\text{V/m}$
3. $\overrightarrow{E}=3\times {10}^{-8}\sin \left[200\pi \right(y+ct\left)\right]\hat{k}\text{V/m}$
4. $\overrightarrow{E}=-9\sin \left[200\pi \right(y+ct\left)\right]\hat{k}\text{V/m}$

Q. In an electromagnetic wave, the phase difference between electric and magnetic field vectors $\overrightarrow{E}\text{and}\overrightarrow{B}$ is-

1. $0$
2. $\frac{\pi }{2}$
3. $\pi$
4. $\frac{\pi }{4}$

Q. The velocity of an electromagnetic wave is parallel to

1. $\overrightarrow{B}\times \overrightarrow{E}$
2. $\overrightarrow{E}\times \overrightarrow{B}$
3. $\overrightarrow{E}$
4. $\overrightarrow{B}$

Q. A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears $2beats/sec$. The oscillation frequency of each tuning fork is $v_0=1400Hz$ and the velocity of sound in air is $350m/s$. The speed of each tuning fork is close to

1. $\frac{1}{2}m/s$
2. $\frac{1}{4}m/s$
3. $1m/s$
4. $\frac{1}{8}m/s$
   

Q. Fundamental frequency of sonometer wire is $n$. If the length, tension and diameter of wire are tripled, the new fundamental frequency is

1. $\frac{n}{3}$
2. $n\sqrt{3}$
3. $\frac{n}{3\sqrt{3}}$
   
4. $\frac{n}{\sqrt{3}}$
   

Q.

An electromagnetic wave in vacuum has the electric and magnetic field $\overrightarrow{E}$ and $\overrightarrow{B}$, which are always perpendicular to each other. The direction of polarization is given by $\overrightarrow{X}$ and that of wave propagation by $\overrightarrow{k}$. Then

1. $\overrightarrow{X}||\overrightarrow{B}and\overrightarrow{k}||\overrightarrow{E}\times \overrightarrow{B}$

2. $\overrightarrow{X}||\overrightarrow{E}and\overrightarrow{k}||\overrightarrow{B}\times \overrightarrow{E}$

3. $\overrightarrow{X}||\overrightarrow{B}and\overrightarrow{k}||\overrightarrow{B}\times \overrightarrow{E}$

4. $\overrightarrow{X}||\overrightarrow{B}and\overrightarrow{k}||\overrightarrow{B}\times \overrightarrow{B}$

Q. A transverse mechanical harmonic wave is travelling on a string. Maximum velocity and maximum acceleration of a particle on the string are $3m/s$ and $90m/s^2$ respectively. If the wave is travelling with a speed of $20m/s$ on the string, then the wave equation is

1. $y=\sin (30t\pm 1.5x)$
2. $y=1.5\sin (30t\pm 0.1x)$
3. $y=0.5\sin (30t\pm 0.1x)$
4. $y=0.1sin(30t\pm 1.5x)$

Q. A glass tube $1.5m$ long and open at both ends, is immersed vertically in a water tank completely. A tuning fork of $660Hz$ is vibrated and kept at the upper end of the tube and the tube is gradually raised out of water. The total number of resonances heard before the tube comes out of water, taking velocity of sound in air $330m/$sec is

1. $4$
2. $8$
3. $6$
4. $12$

Q. The oscillating magnetic field of a plane electromagnetic wave is given as $B=4\times {10}^{–6}\sin [200\pi x–30\times {10}^9\pi t]$ Tesla. The amplitude of electric field is

1. $90\text{V/m}$
2. $600\text{V/m}$
3. $900\text{V/m}$
4. $1200\text{V/m}$

Q. The correct match between the entries in column I and column II are

$I$ Radiation	$II$ Wavelngth
$\left(A\right)$	Microwave	$\left(i\right)$	$100\text{m}$
$\left(B\right)$	Gamma rays	$\left(ii\right)$	${10}^{-15}\text{m}$
$\left(C\right)$	A.M. radio waves	$\left(iii\right)$	${10}^{-10}\text{m}$
$\left(D\right)$	X-rays	$\left(iv\right)$	${10}^{-3}\text{m}$

1. $\text{(A)-(ii), (B)-(i), (C)-(iv), (D)-(iii)}$
2. $\text{(A)-(i), (B)-(iii), (C)-(iv), (D)-(ii)}$
3. $\text{(A)-(iii), (B)-(ii), (C)-(i), (D)-(iv)}$
4. $\text{(A)-(iv), (B)-(ii), (C)-(i), (D)-(iii)}$

Q. Equation of travelling wave on a stretched string of linear density $5g/m$ is $y=0.03\sin (450t-9x)$ where distance and time are measured in$SI$ units. The tension in the string is

1. $10N$
2. $12.5N$
3. $7.5N$
4. $5N$

Q. The faintest sound, the human ear can detect at a frequency of $1kHz$ (for which ear is most sensitive) corresponds to an intensity of about ${10}^{-12}W/m^2$. Assuming the density of air $\cong 1.5kg/m^3$ and velocity of sound in air $\cong 300m/s$, the pressure amplitude and displacement amplitude of the sound will be respectively ___ $N/m^2$ and ____$m$.

1. $2\times {10}^{-5}Pa,\frac{2}{3\pi }\times {10}^{-10}m$
2. $5\times {10}^{-5}Pa,\frac{1}{\pi }\times {10}^{-10}m$
3. $3\times {10}^{-5}Pa,\frac{1}{3\pi }\times {10}^{-10}m$
4. $5\times {10}^{-5}Pa,\frac{4}{3\pi }\times {10}^{-10}m$

Q. The correct figure that shows, schematically, the wave pattern produced by superposition of two waves of frequencies $9\text{Hz}$ and $11\text{Hz}$ is:

1. 
2. 
3. 
4. 

Q.

A plane electromagnetic wave propagating along $y$-direction can have the following pair of electric field $\left(\overrightarrow{E}\right)$ and magnetic field $\left(\overrightarrow{B}\right)$ components

1. $Ex,Bz$or $Ez,Bx$

2. $Ey,Bx$ or $Ex,By$

3. $Ex,By$ or $Ey,Bx$

4. $Ey,By$ or $Ez,Bz$

Q. A tuning fork of frequency $480Hz$ is used in an experiment for measuring speed of sound $\left(v\right)$ in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, $l_1=30cm$ and $l_2=70cm$. Then $v$ is equal to

1. $384m{s}^{-1}$
2. $338m{s}^{-1}$
3. $379m{s}^{-1}$
4. $332m{s}^{-1}$
   

Q. An EM wave from air enters a medium. The electric fields are ${\overrightarrow{E}}_1=E_{01}\hat{x}\cos \left[2\pi v(\frac{z}{c}-t)\right]$ in air and
${\overrightarrow{E}}_2=E_{02}\hat{x}\cos \left[k\right(2z-ct\left)\right]$ in medium, where the wave number $k$ and frequency v refer to their values in air. The medium is non-magnetic. If ${\epsilon }_{r_1}$ and ${\epsilon }_{r_2}$ refer to relative permitivities of air and medium respectively, which of the following options is correct?

1. $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=\frac{1}{4}$
2. $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=\frac{1}{2}$
3. $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=4$
4. $\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=2$

Q. The vibrations of a string of length $60cm$ fixed at both ends are represented by the equation
$y=4\sin \left(\frac{\pi x}{15}\right)\cos \left(96\pi t\right)$, where $x$ and $y$ are in $cm$ and $t$ in 𝑠𝑒𝑐𝑜𝑛𝑑. The maximum displacement (in $cm$) at $x=\frac{5}{2}cm$ is

Q. A stretched string resonates in fundamental node with tuning fork of frequency $512\text{Hz}$ when length of the string is $0.5\text{m}$. The length of the string required to vibrate in resonance with a tuning fork of frequency $256\text{Hz}$ in fundamental node would be

1. $0.25\text{m}$
2. $0.5\text{m}$
3. $1\text{m}$
4. $2\text{m}$

Q. A submarine $\left(A\right)$ travelling at 18 $km/hr$ is being chased along the line of its velocity by another submarine $\left(B\right)$ travelling at 27 $km/hr$. $B$ sends a sonar signal of $500HZ$ to detect $A$ and receives a reflected sound of frequency $v$. The value of $v$ is close to (Speed of sound in water =$1500m/s$

1. $507Hz$
2. $502Hz$
3. $504Hz$
4. $499Hz$
   

Q. A source of sound $S$ of frequency $500Hz$ situated between a stationary observer $O$ and a wall $W$ , moves towards the wall with a speed of $2m/s$ . If the velocity of sound is $332m/s$ , then the number of beats per second heard by the observer is (approximately)

Q. An electromagnetic wave is propagating in vacuum along $z-$axis. The electric field component is given by $E_x=E_{\circ }\sin (kz-\omega t)$, then the magnetic component is,

1. $B_x=\frac{E_{\circ }}{C}\sin (kz-\omega t)$
2. $B_y=\frac{B_{\circ }}{C}\sin (kz-\omega t)$
3. $B_y=\frac{E_{\circ }}{C}\sin (kz-\omega t)$
4. $B_y=B_{\circ }C\sin (kz-\omega t)$

Q. If ${\lambda }_v,{\lambda }_x$ and ${\lambda }_m$ represent the wavelengths of visible light, $X-$ rays and microwaves respectively, then -

1. ${\lambda }_m>{\lambda }_x>{\lambda }_v$
2. ${\lambda }_m>{\lambda }_v>{\lambda }_x$
3. ${\lambda }_v>{\lambda }_x>{\lambda }_m$
4. ${\lambda }_v>{\lambda }_m>{\lambda }_x$

Q. A motor car blowing a horn of frequency $124vib/sec$ moves with a velocity $72km/hr$ towards a tall wall. The frequency of the reflected sound heard by the driver will be (velocity of sound in air is $330m/s$)

1. $132vib/sec$
2. $109vib/sec$
3. $248vib/sec$
4. $140vib/sec$

Q. When we increase the loudness of sound produced by a radio, the property of the sound wave that changes is its

1. amplitude.
2. frequency.
3. speed.
4. wavelength.

Q. $S_1$and $S_2$ are two coherent sources of sound having no initial phase difference. The velocity of sound is $330m/s$. No minima will be formed on the line passing through $S_2$ and perpendicular to the line joining $S_1$ and $S_2$, if the frequency of both the sources is:

1. $60Hz$
2. $50Hz$
3. $70Hz$
4. $80Hz$

Q. A particle is dropped from a height $H$. The de Broglie wavelength of the particle as a function of height is proportional to

1. $H^{\frac{-1}{2}}$
2. $H^0$
3. $H$
4. $H^{\frac{1}{2}}$

Q. Two passenger trains moving with a speed of $108km/\text{hour}$ cross each other. One of them blows a whistle whose frequency is $750Hz$. If sound speed is $330m/s$., then passengers sitting in the other train, after trains cross each other will hear sound whose frequency (in $Hz$.) will be

Q. The siren of an ambulance needs to be a loud and piercing sound. Therefore, its main characteristics should be:

1. High pitch and small amplitude.
2. Low pitch and small amplitude.
3. High pitch and large amplitude.
4. Low pitch and large amplitude.

Q.

A steel wire of mass 4.0 g and length 80 cm is fixed at the two ends. The tension in the wire is 50N. The frequency of the fourth harmonic of the fundamental is

1. 0.25 Hz

2. 25 Hz

3. 250 Hz

4. none of these