Intuition of Wave Speed

Q. For a plane progressive wave represented by, $y=5\sin (100\pi t-0.4\pi x)$, what is the wave velocity (in $\text{m/s}$)?

1. $250$
2. $180$
3. $350$
4. $200$

Q.

Which of the following has the highest energy?

1. X-rays

2. Ultraviolet radiation

3. Gamma rays

4. Infrared radiation.

Q. The displacement of a particle of a string carrying a travelling wave is given by $y=3\sin \left[6.28\right(0.50x-50t\left)\right]$
$(x\to \text{in cm},y\to \text{cm},t\to \text{in second})$.
What would be the speed of the wave?

1. $200{\text{cm s}}^{-1}$
2. $100{\text{cm s}}^{-1}$
3. $150{\text{cm s}}^{-1}$
4. $50{\text{cm s}}^{-1}$

Q. The equation of a travelling wave is y = 60 cos(1800 t - 6x) where y is in microns, t in seconds and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is

1. 3.6 x 10^-11
2. 3.6 x 10^-6
3. 3.6 x 10^-4
4. 3.6

Q. Find the natural frequency of oscillation of spring block system shown.

1. $\frac{7}{\pi }\text{Hz}$
2. $\frac{10}{\pi }\text{Hz}$
3. $\frac{3}{\pi }\text{Hz}$
4. $\frac{5}{\pi }\text{Hz}$

Q.

Two blocks each having a mass of 3.2 kg are connected by awire CD and the system is suspended from the ceiling by another wire AB (figure 15-E5). The linear mass density of the wire AB is $10g{m}^{-1}$ and that of CD is $8g{m}^{-1}.$ Find the speed of a transverse wave pulse produced in AB and in CD.

Q. The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$ here $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is

1. $300\text{m/s}$
2. $30\text{m/s}$
3. $400\text{m/s}$
4. $40\text{m/s}$

Q.

Two parts of a sonometer wire divided by a movable bridge differ in length by $0.2cm$ and produce $1beat/s$ when sounded together. The total length of the wire is $1m$, then the frequencies are

1. $250.5Hz$ and $249.5Hz$

2. $230.5Hz$ and $229.5Hz$

3. $220.5Hz$ and $219.5Hz$

4. $210.5Hz$ and $209.5Hz$

Q. Assertion: In the equation, $y=A\sin (kx-\omega t)$ , particle starts from its mean position $x=0$ and moves towards negative $y-$axis.
Reason: The wave corresponding to given equation is travelling towards positive $x-$direction.

1. Both assertion and reason are correct and reason is the correct explanation of assertion.
2. Both assertion and reason are correct but reason is not a correct explanation of assertion.
3. Assertion is correct but reason is incorrect.
4. Assertion is incorrect but reason is correct.

Q.

A sonometer wire having a length of 1.50 m between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire ?

Q. The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$, where $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is (in $\text{m/s}$)

Q.

A stretched string is forced to transmit transverse waves by means of an oscillator coupled to one end. The string has a diameter of 4mm. The amplitude of the oscillation is ${10}^{-4}m$ and the frequency is 10 Hz. Tension in the string is 100 N and mass density of wire is $4.2\times {10}^{3}kg/m^3$ ​. Find Average energy flow per unit time

1. $5.5\times {10}^{-5}J/s$

2. $6.5\times {10}^{-5}J/s$

3. $7.5\times {10}^{-5}J/s$

4. $4.5\times {10}^{-5}J/s$

Q.
If $S_{2}P-S_{1}P=\frac{\lambda }{6},$ find intensity at point P.

1. $4I_o$
2. $3I_o$
3. $2I_o$
4. $I_o$

Q. How is the frequency of a stretched string related to its tension?

Q. For a given wave , maximum particle velocity is $5$ times the wave velocity corresponding to the equation,
$y=A\sin (5t-0.05x)$ in which $A$ , $x$ are in metres and $t$ is in seconds. The value of $A$ is

Q. The figure shows, at time $t=0\text{second}$, a rectangular and triangular pulse on a uniform wire, approaching each other. The pulse speed (of rectangular and triangular pulse) is $0.5\text{cm/s}$. The resultant pulse at $t=2\text{second}$ is,

1. 
2. 
3. 
4. 

Q. A string is under tension so that its length is increased by $\frac{1}{n}$ times its original length. The ratio of fundamental frequency of longitudinal vibrations and transverse vibrations will be

1. $1:1/\sqrt{(}1+1/n)$
2. $n^2:1$
3. $\sqrt{n}:1$
4. $n:1$

Q. A wave is propagating along x-axis. The displacement of particles of the medium in Z-direction at $t=0$ is given by: $z=exp[-(x+2{)}^2]$ 'x' is in meters. At $t=1s$, the same wave disturbance is given by: $z=exp[-(2-x{)}^2].$ Then, the wave propagation velocity is

1. $4m/s$ in + x direction
2. $4m/s$ in - x direction
3. $2m/s$ in + x direction
4. $2m/s$ in - x direction

Q. A wave $y=a\sin (wt-kx)$ on a string meets with another wave producing a node at $x=0$ .Then the equation of the unknown wave is

1. $y=a\sin (wt+kx)$
2. $y=-a\cos (kx-wt)$
3. $y=a\cos (kx-wt)$
4. $y=-a\sin (kx+wt)$

Q. A wire is stretched between two rigid supports vibrates in its fundamental mode with a frequency of $50Hz$. The mass of the wire is $30g$ and its lines density is $4\times {10}^{-2}kgm{s}^{-1}$. The speed of the transverse wave in the string is:

1. $25m{s}^{-1}$
2. $50m{s}^{-1}$
3. $75m{s}^{-1}$
4. $100m{s}^{-1}$

Q.

The equation of a travelling wave is y = 60 cos (1800t – 6x) where y is in microns, t in seconds and x in metres. The ratio of maximum particle velocity to velocity of wave propagation is

1. 

2. 

3. 

4. 

Q. The equation of a progressive wave is $y=0.03\sin 2\pi [\frac{t}{0.01}-\frac{x}{0.30}]$, where $x$ and $y$ are in metres and $t$ is in seconds. The velocity of propagation of the wave is (in $\text{m/s}$)

Q.

A bar magnet suspended freely in a uniform magnetic field is vibrating with a time period of $3$ seconds. If the field strength is increased to $4$ times of the earlier field strength, the time period will be :

1. $6s$
2. $1.5s$
3. $0.75s$
4. $12s$

Q. Equation of progressive wave is given by, $y=4sin[\pi (\frac{t}{5}-\frac{x}{9})+\frac{\pi }{6}],$ where x and y are in metre. Then

1. $v=5m/s$
2. $A=0.04m$
3. $\lambda =18m$
4. $f=50Hz$

Q. Three blocks I, II & III having the mass of 1.6 kg, 1.6 kg and 3.2 kg respectively are connected as shown in the figure. The linear mass density of the wire AB, CD, and DE are 10 g/m, 8 g/m, and 10 g/m respectively. The speed of a transverse wave pulse produced in AB, CD, and DE are : ($g=10m/{sec}^2$)

1. 80 m/s, 20 $\sqrt{1}0$ m/s, 40 m/s
2. 20 $\sqrt{1}0$ m/s, 40 m/s, 80 m/s
3. 20 $\sqrt{1}0$ m/s in all
4. 80 m/s in all

Q. If $L$ is the length of a stretched wire, $T$ is tension in the wire, $e$ is linear density of wire, the frequency of transverse vibrations of stretched wire is proportional to

1. $L^1{T}^{1/2}{e}^{-1/2}$
2. $L^1{T}^{-1/2}{e}^{-1/2}$
3. $L^{-1}{T}^{1/2}{e}^{-1/2}$
4. $L^{1/2}{T}^1{e}^{-1/2}$

Q. Statement-1 : When a travelling wave is sent along a particular string by oscillating one end, the speed of the wave will increase if we increase the frequency of oscillations.
Statement-2 : If a travelling wave sent along a particular string by oscillating its one end, it is the wavelength of the wave that decreases.

1. If both the statements are true and statement-2 is the correct explanation of statement-1
2. If both the statements are true but statement-2 is not the correct explanation of statement-1
3. If statement-1 is true and statement-2 is false
4. If statement-1 is false and statement-2 is true

Q. Transverse waves are generated in two uniform steel wires A and B of diameters ${10}^{-3}m$ and $0.5\times {10}^{-3}m$ respectively, by attaching their free end to a vibrating source of frequency 500 Hz. The ratio of the wavelengths if they are stretched with the same tension is

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

Q. Linear density of a string is $1.3\times {10}^{-4}kg/m$ and wave equation is $y=0.021\sin (x+30t)$. Find the tension in the string where $x$ in meter, $t$ in sec.

1. $1.17\times {10}^{-2}N$
2. $1.17\times {10}^{-1}N$
3. $1.17\times {10}^{-3}N$
4. None.

Q. Transverse waves are generated in two uniform steel wires A and B of diameters ${10}^{-3}m$ and $0.5\times {10}^{-3}m$ respectively, by attaching their free end to a vibrating source of frequency 500 Hz. The ratio of the wavelengths if they are stretched with the same tension is

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