Chapter 15, Problem 91A

To determine

To design:An experiment to test the formula of speed of a wave on a string; the measurements taken and how to use them to test the formula.

Explanation of Solution

Introduction:

Equation for the speed of a wave on a string

  $v=\sqrt{\frac{F_T}{\mu }}$

Where $F_T$ is the tension in the string and $\mu$ is the mass per unit length of the string.

To test the formula of speed of wave on a string, conduct the following experiment:

Take a string of known length and weight. Fix the string’s two end rigid supports.

Suspend a $2\text{ N}$ weight from the string with the help of a thread. This weight acts as the tension applied on the string. On applying the tension a wave propagates through the string.

To calculate the speed of wave, length and mass of the string must be known. The length can be measured using a scale and the weight using a balance.

To calculate mass from the measured weight, divide the weight by acceleration of gravity.

In the formula

  $v=\sqrt{\frac{F_T}{\mu }}$

$F_T$ is the tension in the string and $\mu$ is the mass per unit length of the string.

The tension in the string is $2\text{ N}$ and $\mu$ can be calculated by dividing the mass of the string by its length.

Knowing $F_T$ and $\mu$ , one can calculate the speed of wave $v$ .

Conclusion:

The speed of wave on a string can be calculated if the tension in the string, length and weight of the string is known.