Chapter 15.2, Problem 20PP

To determine

To Find: The next three harmonics frequency produce with the note.

Answer to Problem 20PP

  $740\text{Hz}$ , $1110\text{Hz}$ , $1480\text{Hz}$

Explanation of Solution

Given:

Frequency, $f=370\text{Hz}$

Calculation:

Violin is a musical instrument made up of string and it behaves as an open pipe resonator. Pitch produced by the violin is equal to the fundamental frequency.

Therefore, first harmonic frequency is itself the fundamental frequency.

  $f_1=370\text{Hz}$

Second harmonic frequency is

  $\begin{array}{l}{f}_2=2f_1\\ f_2=2\times 370\text{Hz}\\ f_2=740\text{Hz}\end{array}$

Third harmonic frequency is

  $\begin{array}{l}{f}_3=3f_1\\ f_3=3\times 370\text{Hz}\\ f_3=1110\text{Hz}\end{array}$

Fourth harmonic frequency is

  $\begin{array}{l}{f}_4=4f_1\\ f_4=4\times 370\text{Hz}\\ f_4=1480\text{Hz}\end{array}$

Conclusion:

The next three harmonics frequency produce with the note are $f_2=740\text{Hz}$ , $f_3=1110\text{Hz}$ , $f_4=1480\text{Hz}$