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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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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