Question

Two steel strings of equal diameter and tension have a length of 0.75 m and 0.95 m respectivelyIf the frequency of the first string is 250 Hz., what is the frequency of the second string?

Answer 1

ANSWER:

155.7 Hz

STEP-BY-STEP EXPLANATION:

We have that the formula between length and frequency is as follows:

$\begin{gathered} \frac{L_2}{L_1}=\sqrt[]{\frac{F_1}{F_2}} \\ L_1=0.75\text{ m} \\ L_2=0.95\text{ m} \\ F_1=250\text{ Hz} \\ \text{ Replacing:} \\ \frac{0.95}{0.75}=\sqrt[]{\frac{250}{F_2}} \\ 1.267=\frac{\: 15.81}{\sqrt[]{F_2}} \\ \sqrt[]{F_2}=\frac{15.81}{1.267} \\ F_2=\mleft(\frac{15.81}{1.267}\mright)^2 \\ F_2=155.7\text{ Hz} \end{gathered}$

The frequency of the second string is 155.7 Hz