Issues with Low Frequency

Q. An electro-magnetic wave is propagating in a medium with a velocity $\overrightarrow{v}=v\hat{i}$ . The instantaneous oscillating electric field of this electromagnetic wave is along $+y$ axis. Then, the direction of oscillating magnetic field of the electromagnetic wave will be along

1. –$z$ direction
2. +$z$ direction
3. –$y$ direction
4. –$x$ direction

Q. The bit rate for a signal, which has a sampling rate of 8 kHz and where 16 quantisation levels have been used is

1. 64000 bits/sec
2. 16000 bits/sec
3. 72000 bits/sec
4. 32000 bits/sec

Q. Which of the following relations is correct with regards to electric and magnetic field oscillation vector in case of $EM$ waves (wave is propagating in the $x$ direction)?

1. $\frac{\partial E}{\partial x}=\frac{\partial B}{\partial t}$
2. $\frac{\partial E}{\partial x}=-\frac{\partial B}{\partial t}$
3. $\frac{\partial E}{\partial t}=\frac{\partial B}{\partial x}{\mu }_0{\epsilon }_0$
4. $\frac{\partial E}{\partial t}=-\frac{\partial B}{\partial x}{\mu }_0{\epsilon }_0$

Q. The poynting vector for an electromagnetic wave is :

1. $\overrightarrow{S}=\overrightarrow{E}\times \overrightarrow{H}$
2. $\overrightarrow{S}=\overrightarrow{E}\times \overrightarrow{B}$
3. $\overrightarrow{S}=(\overrightarrow{E}\times \overrightarrow{H})/2$
4. $\overrightarrow{S}=(\overrightarrow{E}\times \overrightarrow{B})/2$

Q. The electric field associated with an e.m. wave in vacuum is given as $\overrightarrow{E}=40\cos (kz-6\times {10}^{8}t)\hat{i}$, where all quantities are in SI units. The value of the propagation constant $k$ is,

1. $6{\text{m}}^{-1}$
2. $3{\text{m}}^{-1}$
3. $2{\text{m}}^{-1}$
4. $0.5{\text{m}}^{-1}$

Q. If $n_1,n_2,n_3$ be the frequency of the segments of a stretched string, then the frequency $n$ of the string itself in terms of $n_1,n_2$ and $n_3$ is

1. $\frac{(n_1{n}_2+n_2{n}_3+n_1{n}_3)}{n_1{n}_2{n}_3}$
2. $\frac{(n_1{n}_2+n_3{n}_1)}{n_1{n}_2{n}_3}$
3. $\frac{n_1{n}_2{n}_3}{(n_1{n}_2+n_2{n}_3+n_3{n}_1)}$
4. $\frac{n_1{n}_2{n}_3}{(n_1{n}_2+n_3{n}_1)}$

Q. In a half wave rectifier, the r.m.s. value of the a.c. component of the wave is

1. equal to d.c. value
2. more than d.c. value
3. less than d.c. value
4. zero

Q. A tuning fork produces 4 beats/second from the stretched string of a sonometer of length 0.49 m and 0.50 m. Calculate the frequency of the tuning fork.

Q. An EM wave from the air enters a medium. The electric field are
$\overrightarrow{E_1}=E_{01}\hat{x}\cos \left[2\pi f(\frac{z}{c}-t)\right]$
in air and $\overrightarrow{E_2}=E_{02}\hat{x}\cos \left[k(2z-ct)\right]$

in medium, where the wave number $k$ and frequency $f$ refer to the values in air. The medium is non-magnetic. If ${ϵ}_{r1}\text{and}{ϵ}_{r2}$ refer to relative permittivities of air and the medium, which of the following options is correct?

1. $\frac{{ϵ}_{r1}}{{ϵ}_{r2}}=4$
2. $\frac{{ϵ}_{r1}}{{ϵ}_{r2}}=2$
3. $\frac{{ϵ}_{r1}}{{ϵ}_{r2}}=\frac{1}{4}$
4. $\frac{{ϵ}_{r1}}{{ϵ}_{r2}}=\frac{1}{2}$

Q. A ________ filter significantly attenuates all frequencies below $f_c$ and passes all frequencies above $f_c$ :

1. band-pass
2. high-pass
3. low-pass
4. band-low

Q. An $EM$ wave from air enters a medium. The electric fields are $\overrightarrow{E_1}=E_{01}\hat{x}\cos \left[2\pi f(\frac{z}{c}-t)\right]$ 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 $f$ refer to their values in air. The medium is non-magnetic. If ${\epsilon }_{r1}$ and ${\epsilon }_{r2}$ refer to relative permittivities of air and medium respectively, which of the following options is correct?

1. $\frac{{\epsilon }_{r1}}{{\epsilon }_{r2}}=4$
2. $\frac{{\epsilon }_{r1}}{{\epsilon }_{r2}}=2$
3. $\frac{{\epsilon }_{r1}}{{\epsilon }_{r2}}=\frac{1}{4}$
4. $\frac{{\epsilon }_{r1}}{{\epsilon }_{r2}}=\frac{1}{2}$

Q. A wave pulse passing on a string with a speed of 40 cm $s^{-1}$ in the negative x-direction has its maximum at x = 0 at t = 0. Where will this maximum be located at t = 5 s?

Q. The bit rate for a signal, which has a sampling rate of 8 kHz and where 16 quantisation levels have been used is

1. 32000 bits/sec
2. 16000 bits/sec
3. 64000 bits/sec
4. 72000 bits/sec

Q. The energy of the wave that passes through unit area unit time is called as ......................... .

1. Quality
2. Intensity
3. Pitch
4. Amplitude

Q. A wave disturbance in a medium is described by $y(x,t)=0.02cos(50\pi t+\frac{\pi }{2})cos\left(10\pi x\right)$ where $x$ and $y$ are in meters and $t$ in seconds

1. A displacement node occurs at $x=0.15m$
2. An antinode occurs at $x=0.3m$
3. The wavelength of the wave is $0.2m$
4. The speed of the wave is $5.0m/s$

Q. The particle acceleration in a transverse wave is

1. same as wave acceleration.
2. related to particle velocity.
3. is related to particle position.
4. is always zero.

Q. Wave velocity and particle velocity at any instant between t=0 to t=T/4 Iin a progressive wave will be

1. perpendicular to each other
2. parallel to each other
3. changes abruptly
4. none of the above

Q. Particle acceleration in a travelling transverse wave is always is

1. always parallel to particle velocity
2. always anti-parallel to particle velocity
3. can be parallel or anti-parallel to particle velocity
4. None of these

Q. Two pules travelling on the same string are described by
$y_1=\frac{5}{{(3x-4t)}^2+2}$ and $y_2=\frac{-5}{{(3x+4t-6)}^2+2}$
marks the correct statement (s)

1. The direction in which each pulse is travelling $y_1$ is in positive x-axis, $y_2$ is in negative x-axis.
2. The time when the two waves cancel everywhere is 0.75 sec.
3. The point where the two waves always cancel is x=1m
4. Amplitude is different for two waves

Q. Find the number of times intensity is maximum in time interval of $1sec$.

1. $4$
2. $6$
3. $8$
4. $10$