Question

The tension, length, diameter and density of a string B are double than that of another string A. Which of the following overtones of B is same as the fundamental frequency of A?

• A. 1st
• B. 2nd
• C. 3rd
• D. 4th

Answer 1

The correct option is C 3rd

$f=\frac{1}{nL}\sqrt{\frac{T}{\mu }}=\frac{1}{nL}\sqrt{\frac{T}{\rho A}}$

Fundamental Frequency of A$=\frac{1}{L_a}\sqrt{\frac{T_a}{{\rho }_a{A}_a}}$

$\frac{T_b}{T_a}=\frac{l_b}{l_a}=\frac{r_b}{r_a}=\frac{{\rho }_b}{{\rho }_a}=2$

Fundamental frequency of b $f_b=\frac{1}{4}{f}_a$

So third overtone of A will be equal to fundamental frequency of B