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  4. Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is :

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Q. Standing waves are produced in a 10 m long stretched string. If the string vibrates in 5 segments and the wave velocity is 20 m/s, the frequency is :

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Solution:

In the case of standing wave, the length of one segment is $ \frac{\lambda }{2} $ . There are 5 segments and total length of string is 10 m. $ \therefore $ $ 5\frac{\lambda }{2}=10 $ $ \Rightarrow $ $ \lambda =4m $ Frequency, $ n=\frac{v}{\lambda }=\frac{20m/s}{4m}=5Hz $ NOTE: Standing wave is an example of interference. Destructive interference means node and constructive interference means antinode.