Wave Speed expression

Q.

Two strings $A$ and $B$, made of same material, are stretched by same tension. The radius of string $A$ is double the radius of $B$. A transverse wave travels on $A$ with speed $v_A$ and on $B$ with speed $v_B$. The ratio $\left(\frac{v_A}{v_B}\right)$ is

1. 1/2

2. 2

3. 1/4

4. 4

Q. In the above question, if the motion of the pulse and rotation of the loop, both are in same direction then the velocity of the pulse with respect to ground will be:

1. 
2. 
3. 
4. 

Q.

A transverse wave is described by the equation $Y=y_{0}sin2\pi (ft-\frac{x}{\lambda })$. The maximum particle velocity is four times the wave velocity if

1. 

2. 

3. 

4. 

Q. In the above question, if both are in opposite direction, then the velocity of the pulse with respect to ground will be:

1. 
2. 
3. 
4. 

Q. The percentage increase in the speed of transverse waves produced in a stretched string if the tension is increased by $4\%$ will be .

Q.

The extension in a string, obeying Hook's law, is $x$. The speed of sound in the stretched string is $v$. If the extension in the string is increased to $1.5x$, the speed of sound will be :

1. 0.75 v

2. 1.22 v

3. 0.61 v

4. 1.50 v

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. 320 N

2. 400 N

3. 240 N

4. 160 N

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. 6.67 N

3. 8.34 N

4. 9.12 N

Q. A circular loop of rope of length L rotates with uniform angular velocity ω about an axis through its centre on a horizontal smooth platform. Velocity of pulse (with respect to rope) produced due to slight radial displacement is given by

1. 
2. 
3. 
4. 

Q. A copper wire 2.4 mm in diameter is 3m long and is used to suspend an 8kg mass from a beam. If a transverse disturbance is sent along the wire by striking it lightly with a pencil, how fast will the disturbance travel? The density of copper is $8920kg/m^3$. [Assuming tension to be constant in the wire and equal to tension at the lower end]

1. 40.2 m/s
2. 44.5 m/s
3. 15.6 m/s
4. 425 m/s