Question

A second harmonic has to be generated in string of length $l$ stretched between two rigid supports. the point where the string has to be plucked and touched are

• A. plucked at $\frac{l}{4}$ and touch at $\frac{l}{2}$
• B. plucked at $\frac{l}{4}$ and touch at $\frac{3l}{2}$
• C. plucked at $\frac{l}{2}$ and touch at $\frac{l}{2}$
• D. plucked at $\frac{l}{2}$ and touch at $\frac{3l}{2}$

Answer 1

The correct option is A plucked at $\frac{l}{4}$ and touch at $\frac{l}{2}$

To generate the second harmonic in a string of length L is stretched between two rigid supports has to plucked at $\frac{L}{4}$ and touched at $\frac{L}{2}$

For the second harmonic, wavelength ${\lambda }_2$ of the stationary wave will be set up on the corresponds to the frequency, n 2

Thus,

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

This shows that we have an antinode at length L will be $\frac{L}{2}$

This shows that we have antinode at $\frac{L}{4}$.

Option A is correct.