    Question

# A string of length l is fixed at both ends. H is vibrating in its 3rd overtone with maximum amplitude a. What is the amplitude at a distance l/3 from one end?

A

$\frac{\sqrt{3}}{2}a$

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B

$0$

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C

$a$

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D

$\frac{a}{2}$

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Solution

## The correct option is A $\frac{\sqrt{3}}{2}a$Step 1:Given:$x=\frac{l}{3}$$2A=a$$n=3$Step 2:Find:Amplitude.Step 3:Calculate Amplitude:$y=2ASin\left(\frac{\left(n+1\right)\pi x}{l}\right)\mathrm{cos}\omega t\phantom{\rule{0ex}{0ex}}=aSin\left(\frac{\left(3+1\right)\pi ×\frac{l}{3}}{l}\right)\mathrm{cos}\omega t\phantom{\rule{0ex}{0ex}}=aSin\left(\frac{4\pi }{3}\right)\mathrm{cos}\omega t\phantom{\rule{0ex}{0ex}}=-a\frac{\sqrt{3}}{2}\mathrm{cos}\omega t$Hence, Option(A) is correct.  Suggest Corrections  0      Similar questions  Explore more