Transmission of Wave

Q. A particle is moving in a circular path of radius $a$ under the action of an attractive potential energy $U=-\frac{k}{2r^2}$. Its total energy is

1. zero
2. $-\frac{3}{2}\frac{k}{a^2}$
3. $\frac{k}{4a^2}$
4. $\frac{k}{2a^2}$

Q.

What are galvanic and faradic currents?

Q. Equation of a plane progressive wave is given by $y=A_1\text{sin}\pi (t-\frac{x}{3})$. After reflecting from a rarer medium amplitude of reflected wave becomes $A_2$. The equation of the reflected wave can be

1. $A_1\text{sin}\pi (t+\frac{x}{3})$
2. $A_2\text{sin}\pi (t-\frac{k}{3}+1)$
3. $A_2\text{sin}\pi (t+\frac{x}{3})$
4. $A_2\text{cos}\pi (t+\frac{x}{3})$

Q. The energy associated with electric field is $\text{(}{U}_E)$ and with magnetic fields is $\left(U_B\right)$ for an electromagnetic wave in free space. Then

1. $U_E<U_B$
2. $U_E=\frac{U_B}{2}$
3. $U_E>U_B$
4. $U_E=U_B$

Q. Two strings $A$ and $B$ made of same material are stretched by same tension. The radius of cross-section of string $A$ is double the radius of cross-section of string $B$. A transverse wave travels through string $A$ with speed $v_A$ and through string $B$ with speed $v_B$. The ratio $\frac{v_A}{v_B}$ is

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

Q.

Figure (15-E10) shows an aluminium wire of length 60 cm joined to a steel wire of length 80 cm and stretched between two fixed supports. The tension produced is 40 N. The cross-selectional area of the steel wire is $1.0m{m}^2$ and that of the aluminium wire is $3.0m{m}^2$. What could be the minimum frequency of a tuning fork which can produce standing waves in the system with the joint as a node ? The density of aluminium is $2.6gc{m}^{-3}$ and that of steel is $7.8gc{m}^{-3}$

Q. A tuning fork produces waves in a medium. If the temperature of the medium changes, then which of the following will change-

1. Amplitude
2. Frequency
3. Wavelength
4. Time-period

Q.

During the propagation of electromagnetic waves in a medium,

1. Electric energy density is equal to the magnetic energy density.

2. Both electric and magnetic energy densities are zero.

3. Electric energy density is half of the magnetic energy density.

4. Electric energy density is double of the magnetic energy density.

Q. Figure shows a string of linear mass density $1.0\text{g/cm}$ on which a wave pulse is travelling.


Find the time taken by the pulse in travelling through a distance of $50\text{cm}$ on the string. Take $g=10{\text{m/s}}^2$

1. $0.04\text{s}$
2. $0.03\text{s}$
3. $0.05\text{s}$
4. $0.08\text{s}$

Q. The equation of a plane progressive wave is $y=0.09\text{sin}8\pi (t-\frac{x}{20})$. When it is reflected at rigid support, its amplitude become ${\frac{2}{3}}^{rd}$ of its previous value. Then the equation of the reflected wave is

1. $y=0.09\sin 8\pi (t-\frac{x}{20})$
2. $y=0.09\sin 8\pi (t+\frac{x}{20})$
3. $y=0.06\sin 8\pi (t+\frac{x}{20})$
4. $y=-0.06\sin 8\pi (t+\frac{x}{20})$

Q.

Unit of energy density of electromagnetic wave is:

1. $J{m}^{-3}$

2. $J{m}^{-2}$

3. $W{m}^{-2}$

4. None of these

Q. Figure shows an incident pulse $P$ reflected from a rigid support. Which one of the following options represent the reflected pulse?

1. 
2. 
3. 
4. 

Q. 16.In a YDSE , bichromatic light wavelength 400 nm and 560 nm are used . The distance between the slits is equal to 0.1 millimetre and the distance between the plane of the slit and the screen is 1m . Find the minimum distance between the two successive region of complete darkness.

Q. Two strings are attached to each other as shown in the figure. The linear mass density of the second string is four times that of the first string and the boundary between the two strings is at $x=0$. The wave equation of the incident wave at the boundary is $y_i=A_i\cos (k_{1}x-{\omega }_{1}t)$. Then, which of the following correctly represents the equation of the transmitted wave? Assume, tension in the two strings are same.

1. $y_t=\frac{2}{3}{A}_i\cos (k_{1}x-{\omega }_{1}t)$
2. $y_t=\frac{3}{2}{A}_i\cos (k_{1}x-{\omega }_{1}t)$
3. $y_t=\frac{3}{2}{A}_i\cos (2k_{1}x-{\omega }_{1}t)$
4. $y_t=\frac{2}{3}{A}_i\cos (2k_{1}x-{\omega }_{1}t)$

Q. The figure shows at time $t=0\text{sec}$, a rectangular and triangular pulse on a uniform wire. They are approaching each other. The pulse speeds are $0.5\text{cm/s}$ each. The resultant pulse at $t=2\text{sec}$ is

1. 
2. 
3. 
4. 

Q. A composite string is made by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. A transverse wave pulse. $y=\left(6\text{mm}\right)\sin (5t+40x)$, where '$t$' is in seconds and '$x$' is in meters, is sent along the lighter string towards the joint. The joint is at $x=0$. The equation of the wave pulse reflected from the joint is $y=\left(2\text{mm}\right)\sin (5t-40x+\pi )$. The percentage of the power transmitted to the heavier string through the joint is approximately

1. $33\%$
2. $89\%$
3. $67\%$
4. $75\%$

Q. The speed of a transverse wave travelling through a wire having a length $50\text{cm}$and mass $5.0\text{g}$ is $80\text{m/s}$. The area of cross-section of the wire is $1.0{\text{mm}}^2$ and its Young's modulus is $16\times {10}^{11}{\text{N/m}}^2$. Find the extension in the wire with respect to its natural length.

1. $0.01\text{mm}$
2. $0.3\text{mm}$
3. $0.04\text{mm}$
4. $0.02\text{mm}$

Q.

A steel wire has a length of 12.0 m and a mass of 2.10 kg. What should be the tension in the wire so that speed of a transverse wave on the wire equals the speed of sound in dry air at ${20}^{\circ }C=343m{s}^{-1}$

Q. A heavy rope is suspended from a rigid support. A wave pulse is set up at the lowest end, then:

1. The pulse will travel with uniform speed
2. The pulse will travel with increasing speed
3. The pulse will travel with decreasing speed
4. The pulse cannot travel through the rope

Q. If a wave is going from one medium to another, then

1. its frequency changes
2. its wavelength does not change
3. its amplitude may change
4. its speed does not change

Q. A travelling wave is partly reflected and partly transmitted from a rigid boundary. Let $a_i,a_r$ and $a_t$ be the amplitudes of incident wave, reflected wave and transmitted wave and $I_i,I_r$ and $I_t$ be the corresponding intensities. Then, choose the correct alternative.

1. $\frac{I_i}{I_r}={\left(\frac{a_i}{a_r}\right)}^2$
2. $\frac{I_i}{I_t}={\left(\frac{a_i}{a_t}\right)}^2$
3. $\frac{I_r}{I_t}={\left(\frac{a_r}{a_t}\right)}^2$
4. All of these

Q. A string of length $7\text{m}$ has a mass of $0.035\text{kg}$. If the tension in the string is $60.5\text{N}$, then speed of a wave on the string is:

1. $77\text{m/s}$
2. $102\text{m/s}$
3. $110\text{m/s}$
4. $165\text{m/s}$

Q. If $E_0$ and $B_0$ are the amplitudes of electric and magnetic field vectors in an electromagnetic wave, then the ratio of energy densities due to both fields is

1. $1:c$
2. $c:1$
3. $c^2:1$
4. $1:1$

Q.

A $200Hz$ wave with amplitude $1mm$ travels on a long string of linear mass density $6g{m}^{-1}$ kept under a tension of $60N$.

(a) Find the average power transmitted across a given point on the string.

(b) Find the total energy associated with the wave in a $20m$ long portion of the string.

Q. Two strings are attached to each other as shown in the figure. The linear mass density of the second string is $16$ times that of the first string and the boundary between the two strings is at $x=0$. The incident wave is given by $y=0.01\cos (20x-100t)$. Then, the ratio of amplitude of reflected wave to amplitude of transmitted wave is:
[Assume, tension in both the strings is same]

1. $3:2$
2. $5:9$
3. $9:5$
4. $2:3$

Q. A rope of mass $m_0$ and length L is suspended vertically. If a mass m is suspended from the bottom of the rope, find the time for a transverse wave to travel the length of the rope.

1. $\sqrt{\frac{L}{m_{0}g}}(\sqrt{m_0+m}-m)$
2. $\sqrt{\frac{L}{2m_{0}g}}(\sqrt{m_0+m}-m)$
3. $2\sqrt{\frac{L}{m_{0}g}}(\sqrt{m_0+m}+m)$
4. $2\sqrt{\frac{L}{m_{0}g}}(\sqrt{m_0+m}-m)$

Q. A wave travelling on a string is transmitted to other string of different density, gets partially reflected at the junction. The reflected wave is inverted in shape as compared to the incident wave. If the incident wave has wavelength ${\lambda }_1$ and the transmitted wave ${\lambda }_2,$ then

1. ${\lambda }_2>{\lambda }_1$
2. ${\lambda }_2={\lambda }_1$
3. ${\lambda }_2<{\lambda }_1$
4. Cannot be predicted

Q.

The waves used for line-of-sight (LOS communication) is

1. sound waves

2. ground waves

3. sky waves

4. space waves

Q. A dog while barking delivers about 1 mW of power. Assume this power is uniformly distributed over a hemispherical area. Now, 5 dogs start barking at the same time from the same point, each delivering 1 mW of power. What would be the sound level at a distance of 5m? (Take, $lo{g}_{10}\left(6.37\right)=0.8$ and $lo{g}_{10}5=0.7$)

1. 70 dB
2. 80 dB
3. 75 dB
4. 72 dB

Q. When a wave a pulse travelling in a string is reflected from a rigid wall to which string is tied as shown in figure.
For this situation two statements are given below

(i)The reflected pulse will be in same orientation of incident pulse due to a phase change of $\pi$ radians
(ii) During reflection the wall exert a force on string upward direction.
For the above given two statements, choose the correct option given below.

1. Both are wrong
2. Only (i) is true
3. Only (ii) is true
4. Both are true