Question

A second harmonic has to be generated in a string if length l stretched between two rigid supports. The points where the string has to be plucked and touched are respectively

• A. $\frac{l}{4},\frac{l}{2}$
• B. $\frac{l}{4},\frac{3l}{4}$
• C. $\frac{l}{2},\frac{l}{2}$
• D. $\frac{l}{2},\frac{3l}{4}$

Answer 1

The correct option is A $\frac{l}{4},\frac{l}{2}$

To generate the second harmonic is a staring of length stretched between two rigid supports has to plucked at $l/4$ and touched at $l/2$

For second harmonic, wavelength $\left({\lambda }_2\right)$ of the standing waves set up on the corresponds to the $n=2$

Thus, ${\lambda }_n=\frac{2l}{n}\Rightarrow {\lambda }_2=\frac{2l}{2}=l$

This shows that we have an antinode at $l/2$

This shows that we have an node at $l/4$

Option $\left(1\right)$ is correct.