Chapter 15, Problem 60A

To determine

To calculate: The frequency of the lowest three harmonics produced by the instrument.

Answer to Problem 60A

The frequency of the lowest three harmonics is $\underset{\_}{\text{1110 Hz,}1850\text{ Hz},2590\text{ Hz}}$

Explanation of Solution

Given:

Pitch = $\text{370 Hz}$ .

Formula used:

The frequency of the lowest three harmonics of a closed pipe is given by the formula:

  $\text{3}{f}_1,5f_1,7f_1$ respectively.

Calculation:

Assuming $f_1=370\text{ Hz}$ .

The lowest threefrequencies can be calculated as:

  $\begin{array}{l}3f_1=3\times 370=1110\text{ Hz}\\ 5f_1=5\times 370=1850\text{ Hz}\\ 7f_1=7\times 370=2590\text{ Hz}\end{array}$

Conclusion:

The frequency of the lowest three harmonics is $\underset{\_}{\text{1110 Hz,}1850\text{ Hz},2590\text{ Hz}}$ .