Wave Speed expression

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 statements, choose the incorrect one.

1. Points $D,E$ and $F$ have upward (positive) velocity.
2. Points $A,B$ and $H$ have downward (negative) velocity.
3. Points $A$ and $E$ have minimum velocity.
4. Point $C$ and $G$ have zero velocity.

Q.

What is the formula for calculating wave velocity?

Q.

What are the effects of the velocity of sound on changing pressure and temperature?

Q.

What is the effect of rise in temperature on the velocity of sound?

Q. For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is
$\overrightarrow{B}(x,t)=[1.2\times {10}^{-7}\sin (0.5\times {10}^{3}x+1.5\times {10}^{11}t\left)\hat{k}\right]\text{T}$
The instantaneous electric field $\overrightarrow{E}$ corresponding to $\overrightarrow{B}$ is (speed of light $c=3\times {10}^8{\text{ms}}^{-1})$

1. $\overrightarrow{E}(x,t)=[-36\sin (0.5\times {10}^{3}x+1.5\times {10}^{11}t\left)\hat{j}\right]\frac{\text{V}}{\text{m}}$
2. $\overrightarrow{E}(x,t)=[-36\sin (1\times {10}^{3}x+0.5\times {10}^{11}t\left)\hat{j}\right]\frac{\text{V}}{\text{m}}$
3. $\overrightarrow{E}(x,t)=\left[36\sin \right(0.5\times {10}^{3}x+1.5\times {10}^{11}t\left)\hat{k}\right]\frac{\text{V}}{\text{m}}$
4. $\overrightarrow{E}(x,t)=\left[36\sin \right(1\times {10}^{3}x+1.5\times {10}^{11}t\left)\hat{i}\right]\frac{\text{V}}{\text{m}}$

Q. When a wave travels in a medium, the particle displacement is given by the equation $y=a\sin 2\pi (bt-cx)$ where $a$, $b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

1. $c=\frac{1}{\pi a}$
2. $c=\pi a$
3. $b=ac$
4. $b=\frac{1}{ac}$

Q.

An electromagnetic wave of intensity $1400\mathrm{W}/{\mathrm{m}}^2$ falls on a metal surface on an area $1.5{\mathrm{m}}^2$ and is completely absorbed by it. Find the force exerted by the beam.

Q.

A hollow pipe of length$0.8m$ is closed at one end. At its open end, a $0.5m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50N$ and the speed of sound is $320m{s}^{-1}$, the mass of the string is

1. $10g$

2. $20g$

3. $40g$

4. $5g$

Q.

A 4.0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of $19.2\times 10kg{m}^{-1}$. Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of $2.0m{s}^{-2}$. Take $g=10m{s}^{-2}.$

Q. Intensity of sunlight is observed as $0.092{\text{Wm}}^{-2}$ at a point in free space. What will be the peak value of magnetic field at that point ?
$({\epsilon }_0=8.85\times {10}^{-12}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2})$

1. $8.31\text{T}$
2. $5.88\text{T}$
3. $2.77\times {10}^{-8}\text{T}$
4. $1.96\times {10}^{-8}\text{T}$

Q. A uniform rope of mass $0.1\text{kg}$ and length $2.5\text{m}$ hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point $0.5\text{m}$ distance from lower end will be:

1. $5\text{m/s},2.24\text{m/s}$
2. $10\text{m/s},3.23\text{m/s}$
3. $7.5\text{m/s},1.2\text{m/s}$
4. $2.25\text{m/s},5\text{m/s}$

Q. A transverse pulse generated at the bottom of the uniform vertical rope of length $L$ travels in upward direction. The time taken by the pulse to reach the top of the rope will be :

1. $\sqrt{\frac{L}{2g}}$
2. $\sqrt{\frac{2L}{g}}$
3. $\sqrt{\frac{L}{g}}$
4. $\sqrt{\frac{4L}{g}}$

Q. A simple harmonic wave is represented by the relation
$y(x,t)=A\sin 2x(vt-\frac{x}{\lambda })$
If the maximum particle velocity is three times the wave velocity, the wavelength $\lambda$ of the wave is

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

Q.

A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of $60cm{s}^{-1}$ when the car accelerates on a horizontal road. Find the acceleration of the car. Take $g=10m{s}^{-1}$.

Q. A string (fixed at both ends) of length $1\text{m}$ has the mass per unit length $0.1{\text{g cm}}^{-1}$. What would be the frequency of vibration of this string for third overtone under the tension of $400\text{N}$ ?

1. $400\text{Hz}$
2. $50\text{Hz}$
3. $300\text{Hz}$
4. $200\text{Hz}$

Q. In the figure the string has a mass $4.5\text{g}$. How much time will it take for a mass for a traverse disturbance produced at the floor to reach the pulley? (Take $g=10{\text{ms}}^{-2}$)

1. $0.4\text{s}$
2. $0.04\text{s}$
3. $20\text{s}$
4. $0.06\text{s}$

Q. A transverse wave travelling on a taut string is represented by :
$y=0.01\sin 2\pi (10t-x)\to y$ and $x$ are in meters and $t$ in seconds. Then

1. Closest points on the string which differ in phase by ${60}^{\circ }$ are $\left(1/6\right)\text{m}$ apart.
   
2. The speed of the wave is $10\text{m/s}$
3. The phase of a certain point on the string changes by ${120}^{\circ }$ in $\left(1/20\right)$ seconds.
   
4. Maximum particles velocity is $\pi /4\text{m/s}.$

Q. The angle between wave velocity and particle velocity in a travelling wave (Longitudinal or Transverse wave ) may be (in radians)

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

Q.

Consider two points lying at a distance of $10m$ and $15m$ from an oscillating source. If the periodic time of oscillation is $0.05s$ and the velocity of the wave produced is $300m{s}^{-1}$, then what will be the phase difference between the two points?

1. $\mathrm{\pi }$

2. $\frac{\mathrm{\pi }}{6}$

3. $\frac{\mathrm{\pi }}{3}$

4. $\frac{2\mathrm{\pi }}{3}$

Q. If the magnetic field of a plane electromagnetic wave is given by $B=100\times {10}^{-6}\sin [2\pi \times 2\times {10}^5(t-\frac{x}{c})]$ then the maximum electric field associated with it is
(The speed of light $=3\times {10}^8\text{m/s}$)

1. $6\times {10}^4\text{N/C}$
2. $4\times {10}^4\text{N/C}$
3. $3\times {10}^4\text{N/C}$
4. $4.5\times {10}^4\text{N/C}$

Q.

How do you increase the amplitude of a wave?

Q. A plane electromagnetic wave, propagating in space, has an electric field of amplitude $9\times {10}^3\text{V/m}$. The amplitude of the magnetic field is,

1. $2.7\times {10}^{12}\text{T}$
2. $9.0\times {10}^{-3}\text{T}$
3. $3.0\times {10}^{-4}\text{T}$
4. $3.0\times {10}^{-5}\text{T}$

Q. A circular loop of rope of length L rotates with uniform angular velocity ω about an axis through its centre on a horizontal smooth platform. Velocity of pulse (with respect to rope) produced due to slight radial displacement is given by

1. 
2. 
3. 
4. 

Q. The equation of a progressive wave for a wire is :
$y=4\sin \left[\frac{\pi }{2}(8t-\frac{x}{8})\right]$. If $x$ and $y$ are measured in $\text{cm}$ and $t$ is in $\text{seconds},$ then velocity of wave is :

1. $64\text{cm/s}$ along $-x$ direction
2. $32\text{cm/s}$ along $-x$ direction
3. $32\text{cm/s}$ along $+x$ direction
4. $64\text{cm/s}$ along $+x$ direction

Q. If the tension and diameter of a sonometer wire of fundamental frequency $n$ are doubled and density is halved, then its fundamental frequency will become

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

Q.

A wave propagates on a string in the positive x-direction at a velocity v. The shape of the string at $t=t_0$ is given by $g(x,t_0)=Asin\left(\frac{x}{a}\right)$ . Write the wave equation for a general time t.

Q.

A string of mass $3kg$ is under the tension of $400N$. The length of the stretched string is $25cm$. If the transverse jerk is stuck at one end of the string, how long does the disturbance take to reach the other end?

1. $0.043s$

2. $0.055s$

3. $0.034s$

4. $0.065s$

Q. The oscillation frequency of a cyclotron is $10\text{MHz}$. What should be the operating magnetic field for accelerating proton?

1. $0.156\text{T}$
2. $0.256\text{T}$
3. $0.356\text{T}$
4. $0.656\text{T}$

Q.

A sound wave of frequency 100 Hz is travelling in air. The speed of sound in air is $350m{s}^{-1}$. (a) By how much is the phase changed at a given point in 2.5 ms? (b) What is the phase difference at a given instant between two points separated by a distance of 10.0 cm along the direction of propagation?

Q. Distance between the trough and crest of a wave is $1.5\text{m}$ while distance between two crests is $5\text{m}$. Which of the following wavelengths is possible?

1. $\frac{1}{2},\frac{1}{4},\frac{1}{6},...$
2. $1,2,3,...$
3. $1,\frac{1}{3},\frac{1}{5},...$
4. $1,3,5,...$