Question

Two persons are playing shehnai made of the same material. Shehnai I is $1.5$ times the length of shehnai II. Let $f_0^{\left(I\right)}$ and $f_0^{\left(II\right)}$ be the fundamental frequencies of shehnai I and shehnai II respectively. Then:

• A. $3f_0^{\left(II\right)}=f_0^{\left(I\right)}$
• B. $3f_0^{\left(II\right)}=2f_0^{\left(I\right)}$
• C. $2f_0^{\left(II\right)}=3f_0^{\left(I\right)}$
• D. $f_0^{\left(II\right)}=3f_0^{\left(I\right)}$

Answer 1

The correct option is C $2f_0^{\left(II\right)}=3f_0^{\left(I\right)}$

Fundamental frequency is given by $f_o=\frac{v}{2L}$
where $L$ is the length of the pipe.
Let the length of Shehnai II be $L$.
Fundamental frequency $f_o^{\left(II\right)}=\frac{v}{2L}$
Length of Shehnai I is $1.5L$.
Fundamental frequency $f_o^{\left(I\right)}=\frac{v}{2\left(1.5L\right)}=\frac{v}{3L}$
$⟹2f_o^{\left(II\right)}=3f_o^{\left(I\right)}$