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  • A wave disturbance in a medium is described by <img alt="\mathrm{ y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%

A wave disturbance in a medium is described by \mathrm{ y(x, t)=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)} where \mathrm{x \: and \: y} are in metres and \mathrm{t} in second -
 

Option: 1

a hide occurs at \mathrm{ x=1.05 \mathrm{~m}}



 


Option: 2

an antinode occurs at \mathrm{ x=0.03 \mathrm{~m}}
 


Option: 3

The wave length of constituent wave is \mathrm{0.02 \mathrm{~m}}
 


Option: 4

The speed of the constituent wave is \mathrm{5.0 \mathrm{~m} / \mathrm{s}.}


Answers (1)

best_answer

\mathrm{y=0.02 \cos \left(50 \pi t+\frac{\pi}{2}\right) \cos (10 \pi x)}

Case I At node, amplitude \mathrm{=0}

\mathrm{ \cos (10 \pi x)=0 }

\mathrm{ 10 \pi x=\frac{\pi}{2}, \frac{3 \pi}{2}, \ldots .}

\mathrm{ x=\frac{1}{20}=0.05 \mathrm{~m}, 0.15 \mathrm{~m}}

Case II At antinode, amplitude is maximum-

\mathrm{ \cos (10 \pi t)=1 }

\mathrm{ 10 \pi t=0, \pi, 2 \pi }

\mathrm{ x=0,0.1 \mathrm{~m}, 0.2 \mathrm{~m} }

\mathrm{ v=\frac{50 \pi}{10 \pi}=5 \mathrm{~m} / \mathrm{s} }

Hence option 4 is correct.





 

Posted by

Gunjita

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