Speed in a Medium

Q.

The mass per unit length of a uniform wire is$0.135g/cm$. A transverse wave of the form $y=–0.21\sin (x+30t)$is produced in it, where $x$is in meter and$t$ is in second. Then, the expected value of tension in the wire is$x\times {10}^{-2}N$. Value of $x$is __________. (Round-off to the nearest integer)

Q.

Two waves are traveling through the same container of nitrogen gas. Wave $A$ has wavelength $1.5m$ and wave $B$ has wavelength of $4.5m$. The speed of the wave $B$ must be …. the speed of the wave $A$.

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.

The dimensions of $1/{\mu }_0{\epsilon }_0$. where symbols have their usual meanings, are

1. $\left[L^{-1}T\right]$

2. $\left[L^{-2}{T}^2\right]$

3. $\left[L^2{T}^{-2}\right]$

4. $\left[L{T}^{-1}\right]$

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

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. 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. The velocity of sound in air at a certain temperature is $350m{s}^{-1}$. What will be the velocity of sound in helium at the same temperature? $({\gamma }_{air}=\frac{7}{5})$
[molecular mass of air = 29, molecular mass of helium = 4]

1. 1032 m/s
2. 1100 m/s
3. 925 m/s
4. 1513 m/s

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. 0.36 N

3. 0.9 N

4. 3.6 N

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. 0.36 N

3. 0.9 N

4. 3.6 N

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

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

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.

The dimensions of $1/{\mu }_0{\epsilon }_0$. where symbols have their usual meanings, are

1. $\left[L^{-1}T\right]$

2. $\left[L^{-2}{T}^2\right]$

3. $\left[L^2{T}^{-2}\right]$

4. $\left[L{T}^{-1}\right]$

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 becomes half.

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

3. the wavelength and frequency both remain unchanged.

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

Q.

A wave is represented by the equation $y=7sin(7\pi t-0.04\pi x+\frac{\pi }{3})$ x is in metres and t is in seconds. The speed of the wave is

1. $175m/s$

2. $49\pi m/s$

3. $\frac{49}{\pi }m/s$

4. $0.28\pi m/s$

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. A harmonic wave has been set up on a very long string which travels along the length of string. The wave has frequency of 50 Hz, amplitude 1 cm and wavelength 0.5 m. For the above described wave.
Statement I: Time taken by wave to travel a distance of 8 m along the length of string is 0.32 s.
Statement II: Time taken by a point on the string to travel a distance of 8 m, once the wave has reached at that point and sets it into motion is 0.32 s.

1. Both the statements are correct
2. Statement I is correct but Statement II is incorrect
3. Statement I is incorrect but Statement II is correct.
4. Both the statements are incorrect.

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. $v=\frac{1}{2L}\sqrt{\frac{L\rho }{Yl}}$