23. a second harmonic has to be generated in a string of length l stretched between two rigid supports. The point where string has to be plucked and touched are
1.l/4,l/2
2.l/4,3l/4
3.l/2,l/4
4.l/2,3l/4
Correct ans is 1. Plz ans.
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Dear Student,

To produce the second harmonic the staring has to vibrate in two segments of equal length as shown in the figure.



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

The point l/2 is the point of anti-node thus it should be touched at this point.
The point l/4 is the point of the maximum displacement of the string from the mean position, thus to ​produced second harmonic it should be plucked at this poin. 

For ​second harmonic, wavelength (${\lambda }_2$) of the stending waves set up on the corresponds to n = 2. 
Thus, 
$$\begin{gathered} {\lambda }_n=\frac{2l}{n} \\ \Rightarrow {\lambda }_2=\frac{2l}{2}=l \end{gathered}$$
This shows that we have an aninode at l/2 and node at l/4. 

Hence, option (1) is correct.

Regards,