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, $f=\frac{\upsilon }{2L}\dots \left(i\right)$
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
$f^{\prime }=\frac{\upsilon }{\left(L/2\right)}=\frac{2\upsilon }{L}=4\left(\frac{\upsilon }{2L}\right)=4f$ (Using $\left(i\right))$