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Q.

A stretched string of length 200cm supports a stationary wave with points having a displacement amplitude of 1 mm being separated by equal intervals of 20cm. To which overtone do these vibrations belong

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a

3

b

6

c

 5

d

4

answer is D.

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Detailed Solution

Separation between adjacent nodes = separation between two particles in adjacent loops

                                                   \large = \,\frac{\lambda }{2}

From the diagram, \large \frac{\lambda }{2}\, = \,\left( {20 + 20} \right)cm

                          \large \Rightarrow \,\frac{\lambda }{2}\, = \,40cm

\large \therefore  Number of loops formed in the string = \large \frac{{200}}{{\frac{\lambda }{2}}}\, = \,\frac{{200}}{{40}}\, = \,5

So the string is vibrating in 5th harmonic i.e 4th overtone.

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