Speed in a Medium

Q.

Light is an electromagnetic wave. Its speed in vacuum is given by the expression

1. $\sqrt{{\mu }_0{e}_0}$

2. $\sqrt{\frac{{\mu }_0}{e_0}}$

3. $\sqrt{\frac{e_0}{{\mu }_0}}$

4. $\frac{1}{\sqrt{{\mu }_0{e}_0}}$

Q. A rope of uniform mass $m$ and length $L$ is hanging from a support. A block of mass $M$ is attached to the rope at the lower end. If a transverse pulse is produced at the lower end, find the time taken by the pulse to reach the upper end.

1. $2\sqrt{\frac{L}{g}}[\sqrt{(1+\frac{M}{m})}-\sqrt{\frac{M}{m}}]$
2. $\frac{3}{2}\sqrt{\frac{L}{g}}[\sqrt{(2+\frac{M}{m})}-\sqrt{\frac{M}{m}}]$
3. $\frac{3}{2}\sqrt{\frac{L}{g}}[\sqrt{(1+\frac{M}{m})}-\sqrt{\frac{M}{m}}]$
4. $\sqrt{\frac{L}{g}}[\sqrt{(1+\frac{M}{m})}-\sqrt{\frac{M}{m}}]$

Q. An observer standing near the sea shore observes 54 waves per minute. If the wavelength of the water wave is 10 m then the velocity of water wave is

1. 540 ms^-1
2. 5.4 ms^-1
3. 0.184 ms^-1
4. 9 ms^-1

Q. A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength ${\lambda }_1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is ${\lambda }_2$. The ratio $\frac{{\lambda }_2}{{\lambda }_1}$ is

1. $\sqrt{\frac{m_1+m_2}{m_2}}$
2. $\sqrt{\frac{m_1}{m_2}}$
3. $\sqrt{\frac{m_1+m_2}{m_1}}$
4. $\sqrt{\frac{m_2}{m_1}}$

Q.

Both the strings, shown in figure, are made of same material and have same cross-section. The pulleys are light. The wave speed of a transverse wave in the string $AB$ is $v_1$ and in $CD$ it is $v_2$. Then $\frac{v_1}{v_2}$ is

1. 1

2. 2

3. 

4. 

Q. If the frequency of a wave is increased by $25\%$ in the same medium. The change in its wavelength will be

1. increase of $20\%$
2. decrease of $20\%$
3. increase of $25\%$
4. decrease of $25\%$

Q.

The linear density of a vibrating string is ${10}^{-4}kg/m$. A transverse wave is propagating on the string, which is described by the equation y = 0.02 sin (x + 30 t), where x and y are in meters and time t in seconds. Then tension in the string is

1. 0.09 N

2. 3.6 N

3. 0.36 N

4. 0.9 N

Q.

A string of length 20 cm and linear mass density $0.40gc{m}^{-1}$ is fixed at both ends and is kept under a tension of 16 N. A wave pulse is produced at t = 0 near an end as shown in figure (15-E3), which travels towards the other end. (a) When will the string have the shape shown in the figure again ? (b) Sketch the shape of the string at a time half of that found in part (a).

Q. Speed of sound in a gas at ${27}^{\circ }C$ is $360\text{m/s}$. Its speed at ${37}^{\circ }C$ is

1. $366\text{m/s}$
2. $372\text{m/s}$
3. $363\text{m/s}$
4. $360\text{m/s}$

Q. Transverse waves travel with a speed of $40\text{m/s}$ in a string under a tension of $12\text{N}$. What tension is required for a wave speed of $60\text{m/s}$ in the same string?

1. $25\text{N}$
2. $29\text{N}$
3. $27\text{N}$
4. $21\text{N}$

Q. Under standard conditions the gas density is 1.3 $\frac{mg}{c{m}^3}$ and the velocity of sound propagation in it is 330 $\frac{m}{s}$, then the number of degrees of freedom of gas is.

Q.

What is the relation between frequency and wavelength?

Q. A wire is $4\text{m}$ long and has a mass of $0.2\text{kg}$. The wire is kept horizontally. A transverse pulse is generated by plucking one end of the taut (tight) wire. The pulse makes four trips back and forth along the
cord in $0.8\text{sec}$. The tension is the cord will be

1. $80\text{N}$
2. $160\text{N}$
3. $240\text{N}$
4. $320\text{N}$

Q.

A block M hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to a fixed rigid support at $O$. A transverse wave pulse (Pulse 1) of wavelength ${\lambda }_0$ is produced at point $O$ on the rope. The pulse takes time $T_{OA}$ to reach point $A$. If the wave pulse of wavelength ${\lambda }_0$ is produced at point $A$ (Pulse 2) without disturbing the position of $M$ it takes time $T_{AO}$ to reach point $O$. Which of the following options is/arc correct?

1. The time $T_{AO}=T_{OA}$

2. The velocities of the two pulses (Pulse 1 and Pulse 2) are same at the midpoint of rope

3. The wavelength of Pulse 1 becomes longer when it reaches point A.

4. The velocity of any pulse along the rope is independent of its frequency and wavelength.

Q. A wave pulse starts propagating in the x-direction along a non-uniform wire of length $20\text{m}$ with mass per unit length given by $\mu ={\mu }_0+ax$ and under a tension of $400\text{N}$. Find the time taken by the pulse to travel from the lighter end $(x=0)$ to the heavier end. ${\mu }_0={10}^{-2}\text{kg/m}$ and $a=16\times {10}^{-3}{\text{kg/m}}^2$

1. 0.4 sec
2. 0.8 sec
3. 1 sec
4. 0.6 sec

Q. A ring of mass $m$ and radius $R$ rotates about an axis passing through its centre and perpendicular to its plane with angular velocity $\omega$. Find the velocity of transverse pulse in the ring.

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

Q. A wave pulse starts propagating in the positive $x-$ direction along a non-uniform wire of length $10\text{m}$ with a mass per unit length given by $m=m_0+\alpha x$ and under a tension of $100\text{N}$. Find the time taken by the pulse in seconds to travel from the lighter end $x=0$ to the heavier end. ($m_0={10}^{-2}\text{kg/m}$ and $\alpha =9\times {10}^{-3}{\text{kg/m}}^2$). Answer upto 2 decimal places.

Q. On December 2006, a great earthquake occurred off the coast of Sumatra and triggered immense waves (Tsunami) that killed some 200, 000 people. Satellites observing these waves from space measured 800 km from one wave crest to the next and a period between waves of 1 hr. what was the speed of the wave?

1. 400 km/hr

2. 1600 km/hr

3. 800 km/hr

4. Data insufficient

Q.

Equation of travelling wave on a stretched string of linear density $5\raisebox{1ex}{$g$}\!\left/ \!\raisebox{-1ex}{$m$}\right.$ is $y=0.03\sin \left(450t-9x\right)$ where distance and time are measured in $SI$ units. The tension in the string is:

1. $12.5N$

2. $7.5N$

3. $10N$

4. $5N$

Q. Two points on string are being observed as a travelling wave passes them. The points are at $x_1=0and{x}_2=lm$, the transverse motions of two points are found to be as follows $y_1=Asin\left(3\pi t\right)and{y}_2=Asin(3\pi t+\frac{\pi }{8})$ ; t is in seconds and y in metre. Mark correct options

1. Frequency of wave is 3 HZ
2. Frequency of wave is 1.5 Hz
3. Wavelength may be 16 m
4. Wavelength may be $\frac{16}{15}m$

Q. Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 4.0 s. When one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves. Determine the speed of the wave.

1. 4 m/s
2. 2.5 m/s
3. 5 m/s
4. 40 m/s

Q. The speed of a transverse wave, travelling on a wire having a length of $100\text{cm}$ and mass $10\text{g}$ is $160\text{m/s}$. The area of cross-section of the wire is $2{\text{mm}}^2$ and its Young's modulus is $32\times {10}^{11}{\text{N/m}}^2$. Find the extension of the wire from its natural length.

1. $0.08\text{mm}$
2. $0.04\text{mm}$
3. $0.02\text{mm}$
4. $1\text{mm}$

Q. If the medium changes, for the same wave the frequency remain the same but the speed changes because the wave speed apart of frequency also depends upon:

1. All of them
2. Amplitude
3. Frequency
4. Wavelength

Q.

An electromagnetic wave of frequency v = 3 MHz passes from vacuum into dielectric medium with permittivity $ϵ=4.0$ Then

1. the wavelength is doubled and the frequency remains the same.

2. the wavelength is doubled and the frequency becomes half.

3. the wavelength and frequency both remain unchanged.

4. the wavelength is halved but the frequency remains the same.

Q. What is the relation between frequency $\left(\nu \right)$, wavelength $\left(\lambda \right)$ and speed of the wave $\left(c\right)$ ?

1. $\nu =c\lambda$
2. $\nu =\frac{2c}{\lambda }$
3. $\nu =\frac{c}{\lambda }$
4. $\nu =\frac{\lambda }{c}$

Q. One meter long (both ends open) organ pipe is kept in a gas that has double the density of air at $\text{STP}$. Assuming the speed of sound of air at $\text{STP}$ is $300{\text{ms}}^{-1}$, the frequency difference between the fundamental and second harmonic of the pipe is_____$\text{Hz}$.

Q.

The downhill movement of masses of rock debris and other materials under the direct influence of gravity is ____

Q. Laminar flows takes place between two parallel plates. The distance between the plates is $B$. The minimum depth of flow from the bottom plate where local velocity is equal to $3/4^{th}$ the average velocity of flow is kB. The value of k (correct upto two decimal place) is ____.

1. 0.14

Q. Two independent harmonic oscillators of equal mass are oscillating about the origin with angular frequencies ${\omega }_1$ and ${\omega }_2$ and have total energies $E_1$ and $E_2$, respectively. The variations of their momenta $p$ with positions $x$ are shown in the figures. If $\frac{a}{b}=n^2$ and $\frac{a}{R}=n$, then the correct equation(s) is(are):

1. $E_1{\omega }_1=E_2{\omega }_2$
2. $\frac{{\omega }_2}{{\omega }_1}=n^2$
3. ${\omega }_1{\omega }_2=n^2$
4. $\frac{E_1}{{\omega }_1}=\frac{E_2}{{\omega }_2}$

Q. Draw a neat sketch of Ruby Laser. Explain its working with the help of energy level diagram.