Speed in a Medium

Q.

The equation of a progressive wave is $y=0.02sin2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$ here x and y are in metres and t is in seconds. The velocity of propagation of the wave is

1. 300 m/s

2. 30 m/s

3. 400 m/s

4. 40 m/s

Q.

The speed of a wave on a string is $150\mathrm{m}/\mathrm{s}$ when the tension is $120\mathrm{N}$. The percentage increase in the tension in order to raise the wave speed by $20\%$ is

1. $10\%$

2. $20\%$

3. $40\%$

4. $44\%$

Q.

A string is producing transverse vibration whose equation

is y = 0.021 sin ( x + 30 t ) Where x and y are in meters and t is in seconds. If

the linear density of the string is 1.3 $\times {10}^{-4}$ kg/m, then the tension in the string

in N will be

[RPET 1999; RPMT 2002]

1. 10

2. 0.5

3. 1

4. 0.117

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.

An electromagnetic wave of frequency $f=3.0MHz$ passes from vacuum into a dielectric medium with permittivity $\epsilon =4.0$. Then

1. Wavelength is doubled and the frequency remains unchanged

2. Wavelength is doubled and frequency becomes half

3. Wavelength is halved and frequency remains unchanged

4. Wavelength and frequency both remain unchanged

Q. A wire of density $\rho$ is stretched between two clamps a distance $L$ apart, while being subjected to an extension $l$. Y is the Young's modulus of the material of the wire. The lowest frequency of transverse vibrations of the wire is given by

1. $v=\frac{1}{2L}\sqrt{\frac{YL}{l\rho }}$
2. $v=\frac{1}{2L}\sqrt{\frac{Y\rho L}{l^2}}$
3. $v=\frac{1}{2L}\sqrt{\frac{Yl}{L\rho }}$
4. $v=\frac{1}{2L}\sqrt{\frac{L\rho }{Yl}}$

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. [Assume extension is very less as compared to the length of the wire]

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

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

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

Q.

The equation $\varphi (x,t)=jsin\left(\frac{2\pi }{\lambda }vt\right)cos\left(\frac{2\pi }{\lambda }x\right)$ represents

[MNR 1994]

1. Transverse progressive wave

2. Longitudinal progressive wave

3. Transverse stationary wave

4. Longitudinal stationary wave

Q. A uniform rope of length $10\text{m}$ and mass $15\text{kg}$ hangs vertically from a rigid support. A block of mass $5\text{kg}$ is attached to the free end of the rope. A transverse pulse of wavelength $0.08\text{m}$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope will be
$($Take $g=10{\text{m/s}}^2)$

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

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

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

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. The mathematical form of three travelling waves are given by
$Y_1=\left(2cm\right)sin(3x-6t)Y_2=\left(3cm\right)sin(4x-12t)and{Y}_3=\left(4cm\right)sin(5x-11t)$
of these waves,

1. Wave 1 has greatest wave speed and greatest maximum transverse string speed
2. Wave 2 has greatest wave speed and wave 1 has greatest maximum transverse string speed
3. Wave 3 has greatest wave speed and wave 1 has greatest maximum transverse string speed
4. Wave 2 has greatest wave speed and wave 3 has greatest maximum transverse string speed.

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.

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 $g(x,t_0)$ = A sin $\left(\frac{x}{a}\right)$ Write the wave equation for a general time t.

1. $Asin[\frac{x}{a}-v(t-t_0\left)\right]$

2. $Asin\left[\frac{x-v(t-t_0)}{a}\right]$

3. $Asin\left[\frac{x+v(t-t_0)}{a}\right]$

4. None of these

Q. Given below are some functions of x and t to represent the displacement (transverse or longitudinal ) of an elastic wave. State which of these represent (i) a travelling wave (ii) a stationary wave or (iii) none at all:
(a) $y=2cos\left(3x\right)\sin \left(10t\right)$
(b) $y=2\sqrt{x-vt}$
(c) $y=3\sin (5x-0.5t)+4\cos (5x-0.5t)$
(d) $y=cosxsint+cos2xsin2t$