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Questions  

A string is rigidly tied at two ends and its equation of vibration is given by y=cos2πt sin2πx.  Then minimum length of string is 

a
1 m
b
12 m
c
5 m
d
2π m

detailed solution

Correct option is B

Given equation of stationary wave is y=sin2πx cos2πt, comparing it with standard equation y=2Asin2πxλcos2πvtλWe have 2πxλ=2πx⇒λ=1mMinimum distance of string (first mode) Lmin =λ2=12m

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A wire having a linear density of 5 g/m is stretched between two rigid supports with a tension of 450 N. It is observed that the wire resonates at a frequency of 420 Hz. The next highest frequency at which the same wire resonates is 490 Hz. Find the length of the wire. (in m)


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