Chapter 11, Problem 52P

To determine

To Find: The frequency of the first four harmonics.

Answer to Problem 52P

The frequency of the first four harmonics are as follows. $f_1=440\text{ Hz, }{f}_2=880\text{ Hz, }{f}_3=1320\text{ Hz, }{f}_4=1760\text{ Hz}$ .

Explanation of Solution

Given info:

Frequency of violin string, $f=440\text{ Hz}$

Formula used:

Write the expression for nth frequencies.

  $f_n=n\times f$

Calculation:

Frequency of the harmonic string are fixed at both ends. Substitute the value of n = 1, 2, 3 and 4 in the above formula,

  $\begin{array}{l}{f}_1=1\times 440=440\text{ Hz}\\ f_2=2\times 440=880\text{ Hz}\\ f_3=3\times 440=1320\text{ Hz}\\ f_4=4\times 440=1760\text{ Hz}\end{array}$

Conclusion:

Thus, the frequency of the first four harmonics are as follows, $f_1=440\text{ Hz, }{f}_2=880\text{ Hz, }{f}_3=1320\text{ Hz, }{f}_4=1760\text{ Hz}$ .