Question

A sonometer wire of length $L$, has fundamental frequency $f$. If it is plucked at $\frac{L}{8}$ from the fixed end, then the frequency of the wire is

• A. $f$
• B. $2f$
• C. $3f$
• D. $4f$

Answer 1

Answer: (D)

When a wire is plucked at $\frac{L}{8}$ from the fixed end, fourth harmonic is produced as shown in the figure

Fundamental frequency, $f =\frac{\upsilon}{2L} \ldots\left(i\right)$
where $ \upsilon$ is the velocity of sound
A point where wire is plucked antinode is produced
Distance between node and antinode is $\frac{\lambda}{4}$
$\therefore \, \frac{\lambda}{4}=\frac{L}{8}$ or $\lambda=\frac{L}{2}4$
$\therefore $ The frequency of the wire is
$f' =\frac{\upsilon}{\left(L /2\right)}=\frac{2\upsilon}{L}=4 \left(\frac{\upsilon}{2L}\right)=4f $ (Using $\left(i\right))$