Question

Which of the following makes the velocity of a wave in a stretched string greater? *

1/1

shortening the string

plucking harder

A tightening

using a thicker string​

Answer 1

Which of the following makes the velocity of a wave in a stretched string greater? *1/1

a. shortening the string

b. plucking harder

c. A tightening

d. using a thicker string

answer: option B. Plucking harder

mark as brainlist please

Answer 2

Explanation:

• A spring is an example of a wave motion, as it vibrates/ oscillates to and fro about a mean position.

• A spring, when stretched manually from its mean position gains a certain potential energy with increase in distance from the mean position. This potential energy is given by

      $E=\frac{1}{2}kx^{2}$  where, k is the spring constant and x is the stretched length.

• When, this spring is released from a position of maximum displacement from the mean position called as amplitude, all of the potential energy gets converted into the kinetic energy.

• We know, kinetic energy is the energy possessed by an object by virtue of its velocity.

• This velocity of the spring in wave motion is given by,

         $v=\sqrt{\frac{T}{u}$

where, T is the qualitative value of the spring also can be said as elasticity or tension in the string, and μ is the mass per unit length of the spring.

$v=\sqrt{\frac{TL}{M} }$

According to the question,

• Shortening the string

False.From the equation of velocity, velocity is directly proportional to the length of the string. Decreasing the length of the string, the velocity of the string shall decrease.

• Plucking harder

True.Pulling the spring harder will result in gaining more potential energy hence, the elasticity of the spring will increase and thus,the tension in the spring will increase. Hence, this increases the velocity of the spring.

• Tightening

False.Velocity of the wave does not anywhere depend upon the strength with which the spring is attached to a stationary wall. Hence, tightening the spring will not increase the velocity of the spring.

• Using a thicker string

False. According to the equation of velocity of spring, the velocity is inversely proportional to the mass and hence volume of the spring. Increasing the radius of the spring will result in decrease in the velocity of the spring.