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

155.7 Hz

Explanation:

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

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

The frequency of the second string is 155.7 Hz