Wave Speed expression

Q.

A wave moves with speed 300 m/s on a wire which is under a tension of 500 N. Find how much the tension must be changed to increase the speed to 312 m/s?

1. 7.12 N

2. 8.34 N

3. 9.12 N

4. 6.67 N

Q.

If the tension of sonometer's wire increases four times then the fundamental frequency of the wire will increase by

[RPMT 1999]

1. 2 times

2. 1/2 times

3. None of the above

4. 4 times

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. 

2. 

3. 1

4. 2

Q. For a damped oscillator k = 85 N/m, m = 250g and b = 70 g/s. What is the period of oscillation- (1) 0.34 sec. (2) 0.68 sec. (3) 0.20 sec. (4) cannot predict

Q. frequency of simple pendulum is 50 oscillations per minute. if its length is doubled and the bob is replaced by another having half the weight the new frequency of oscillations per minute will be nearly

Q. A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?

Q. 78.A tuning fork A , marked 512 Hz produces 5 beats per second when sounded with another tuning fork B . If B is loaded with wax , the number of beats is again 5 per second. What is the frequency of the tuning fork B when not loaded .??

Q. 31.A tuning fork give 4 beats with 50 cm length of the sonometer wire if the length of the wire shortened by 1 cm but it still produces 4 beats than what is the frequency of the fork

Q. The speed of a wave in a string is independent of its wavelength.

1. True
2. False

Q. A uniform rope of mass $0.1\text{kg}$ and length $2.5\text{m}$ hangs from ceiling. The speed of transverse wave in the rope at upper end and at a point $0.5\text{m}$ distance from lower end will be:

1. $5\text{m/s},2.24\text{m/s}$
2. $10\text{m/s},3.23\text{m/s}$
3. $7.5\text{m/s},1.2\text{m/s}$
4. $2.25\text{m/s},5\text{m/s}$

Q. 110.A tunning fork vibrating with a sonometer having a wire of length 20cm produces 5 beats /sec. The beats frequency doesnt change if the length of the wire is changed to 21cm. The frequency of the tunning fork must be 1) 200Hz 2) 210Hz 3) 205Hz 4) 215H

Q. A loop of a string of mass per unit length $\mu$ and radius $R$ is rotated about an axis passing through its centre and perpendicular to its plane with an angular velocity $\omega$. A small disturbance is created in the loop having the same sense of rotation w.r.t the string. The linear speed of the disturbance for a stationary observer is

1. $\omega R$
2. $2\omega R$
3. $3\omega R$
4. Zero

Q. A simple harmonic wave is represented by the relation
$y(x,t)=A\sin 2\pi (vt-\frac{x}{\lambda })$
If the maximum particle velocity is three times the wave velocity, the wavelength $\lambda$ of the wave is

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

Q. As the wavelength of a wave in a uniform medium increases, its frequency will provided the velocity of wave remains constant.

1. decrease
2. increase
3. remain the same

Q.

A wave moves with speed 300 m/s on a wire which is under a tension of 500 N. Find how much the tension must be changed to increase the speed to 312 m/s?

1. 6.67 N

2. 7.12 N

3. 8.34 N

4. 9.12 N

Q. Frequency of a wave is the number of successive crests (or troughs) passing a given point in 1 second.

1. False
2. True

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

1. $3.6$
2. $3.6\times {10}^{-6}$
3. $3.6\times {10}^{-11}$
4. $3.6\times {10}^{-4}$

Q. A string (fixed at both ends) of length $1\text{m}$ has the mass per unit length $0.1{\text{g cm}}^{-1}$. What would be the frequency of vibration of this string for third overtone under the tension of $400\text{N}$ ?

1. $400\text{Hz}$
2. $300\text{Hz}$
3. $50\text{Hz}$
4. $200\text{Hz}$

Q. Shape of a transverse wave at time $t=t_0$ is shown in the figure given below.

At $x=x_0$ and time $t=t_0$, slope of the wave curve is $5$. Find the ratio of particle velocity to the wave velocity at $x=x_0$.

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

Q. The equation of a wave disturbance is given as y =Asin(2pi+kx ).if velocity is 100m/s then the value of propogation constant

Q. The angle between wave velocity and particle velocity in a travelling wave (Longitudinal or Transverse wave ) may be (in radians)

1. $0$
2. $\frac{\pi }{4}$
3. $\frac{\pi }{2}$
4. $\pi$

Q. A transverse pulse generated at the bottom of the uniform vertical rope of length $L$ travels in upward direction. The time taken by the pulse to reach the top of the rope will be :

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

Q. When a wave travels in a medium, the particle displacement is given by the equation $y=a\sin 2\pi (bt-cx)$ where $a$, $b$ and $c$ are constants. The maximum particle velocity will be twice the wave velocity if

1. $c=\frac{1}{\pi a}$
2. $c=\pi a$
3. $b=ac$
4. $b=\frac{1}{ac}$

Q.

Two blocks of masses 40 kg and 20 kg are connected by a wire that has a linear mass density of 1 g/m. These blocks are being pulled across horizontal frictionless floor by horizontal force F that is applied to 20 kg block. A transverse wave travels on the wave between the blocks with a speed of 400 m/s (relative to the wire). The mass of the wire is negligible compared to the mass of the blocks. The magnitude of F is

1. 160 N

2. 240 N

3. 320 N

4. 400 N

Q. In the figure the string has a mass $4.5\text{g}$. How much time will it take for a mass for a traverse disturbance produced at the floor to reach the pulley? (Take $g=10{\text{ms}}^{-2}$)

1. $0.04\text{s}$
2. $20\text{s}$
3. $0.4\text{s}$
4. $0.06\text{s}$

Q. Shape of a transverse wave at time $t=t_0$ is shown in the figure given below.

At $x=x_0$ and time $t=t_0$, slope of the wave curve is $5$. Find the ratio of particle velocity to the wave velocity at $x=x_0$.

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

Q.

explain frequency with diagram ?

Q. Speed of sinusoidal transverse wave does not depend upon

1. time period
2. frequency
3. initial phase constant
4. wave length