Chapter 16, Problem 81A

To determine

The speed of the waves on the string.

Answer to Problem 81A

  $\text{ 528}\text{m/s}$

Explanation of Solution

Given:

The length of guitar string, $l=60.0\text{cm}$

The frequency of the note, $f=440\text{Hz}$

Formula used:

  $\text{Frequency = }\frac{\text{Speed}}{\text{wavelength}}$

Calculation:

Since the guitar string is plucked in the middle, thus the wavelength of the wave will be,

  $\lambda =2l=120\text{cm = 1}\text{.2}\text{}\text{m}$

Then, using the given values, the speed of the waves on the string will be,

  $\begin{array}{c}\text{Speed = Frequency}\times \text{Wavelength}\\ \text{= 440}\times \text{1}\text{.2}\\ \text{= 528}\text{m/s}\end{array}$

Conclusion:

Hence, the speed of the waves on the string is $\text{ 528}\text{m/s}$ .