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  • A stationary wave set up on a string have the equation <img alt="\mathrm{y=(2 \mathrm{~mm}) \sin \left[\left(6.25 \mathrm{~m}^{-1}\right)\right.x \cos (\omega t)]}" src="https://entrancecorner.onco

A stationary wave set up on a string have the equation \mathrm{y=(2 \mathrm{~mm}) \sin \left[\left(6.25 \mathrm{~m}^{-1}\right)\right.x \cos (\omega t)]} This stationary wave is created by two identical waves, of amplitude \mathrm{A} each moving in opposite directions along the string. then -
 

Option: 1

\mathrm{A=2 \mathrm{~mm}}
 


Option: 2

\mathrm{A=4 \mathrm{~mm}}
 


Option: 3

The smallest length of string is \mathrm{50 \mathrm{~cm}.}
 


Option: 4

The smallest length of string is \mathrm{2 \mathrm{~m}.}


Answers (1)

best_answer

\mathrm{ A=\frac{2}{2}=1 \mathrm{~mm} . }
from the data, we can see that \mathrm{ k=6.25 \mathrm{~m}^{-1}. } smallest length of string is equivalent to a single loop or length of string equal to \mathrm{ \frac{\lambda}{2} or \frac{\pi}{k} }.

\mathrm{ \therefore L_{\text {min }}=\frac{\pi}{k}=\frac{\pi}{6.25} =0.5 \mathrm{~m} }

                                       \mathrm{ =50 \mathrm{~cm} }

Hence option 3 is correct.

 

Posted by

Pankaj Sanodiya

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