Consider two waves passing through the same string. The principle of superposition for displacement says that the net displacement of a particle on the string is the sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for:

1.	both the velocity but not for the kinetic energy
2.	the velocity but not for the kinetic energy
3.	the kinetic energy but not for the velocity
4.	neither the velocity nor the kinetic energy

Two wave pulses travel in opposite directions on a string and approach each other. The shape of one pulse is inverted with respect to the other.

1. The pulses will collide with each other and vanish after collision

2. The pulses will reflect from each other, i.e., the pulse going towards right will finally move towards left and vice versa

3. The pulses will pass through each other but their shapes will be modified

4. The pulse will pass through each other without any change in their shapes

Two periodic waves of amplitudes \(A_1\) and \(A_2\) pass through a region. If \(A_1>A_2​​\), the difference in the maximum and minimum resultant amplitude possible is: 
1. \(2A_1\) 
2. \(2A_2\) 
3. \(A_1+A_2​​\) 
4. \(A_1-A_2​​\)

Two waves of equal amplitude A, and equal frequency travel in the same direction in a medium. The amplitude of the resultant wave is

1. 0

2. A

3. 2A

4. between 0 and 2A

Two sine waves travel in the same direction in a medium. The amplitude of each wave is \(A\) and the phase difference between the two waves is \(120^\circ.\) The resultant amplitude will be:
1. \(A\)
2. \(2A\)
3. \(4A\)
4. \(\sqrt2 A\)

The fundamental frequency of a string is proportional to:

A tuning fork of frequency 480 Hz is used to vibrate a sonometer wire having natural frequency 240 Hz. The wire will vibrate with a frequency of

1. 240 Hz

2. 480 Hz

3. 720 Hz

4. will not vibrate

A tuning fork of frequency \(480\) Hz is used to vibrate a sonometer wire having natural frequency \(410\) Hz. The wire will vibrate with a frequency:

A sonometer wire supports a \(4~\text{kg}\) load and vibrates in fundamental mode with a tuning fork of frequency \(416~\text{Hz}.\) The length of the wire between the bridges is now doubled. In order to maintain fundamental mode, the load should be changed to:
1. \(1~\text{kg}\)
2. \(2~\text{kg}\)
3. \(8~\text{kg}\)
4. \(16~\text{kg}\)