Question

If the frequency of the $2^{nd}$ and $5^{th}$ harmonics of string fixed at both ends differ by $108\text{Hz}$. What is the fundamental frequency of the string?

• A. $18\text{Hz}$
• B. $9\text{Hz}$
• C. $36\text{Hz}$
• D. $72\text{Hz}$

Answer 1

The correct option is C $36\text{Hz}$

Frequency of vibration in a string fixed at both ends is given by
$f=\frac{nv}{2L}$
Fundamental frequency $f=\frac{v}{2L}$
For second harmonic, $f_2=\frac{2v}{2L}=2f$
For fifth harmonic, $f_5=\frac{5v}{2L}=5f$

From the data given in the question,
$5f-2f=108\Rightarrow 3f=108$
$\Rightarrow f=36\text{Hz}$