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The equation of  a wave on a string of linear mass density 0.04 kg m -1 is given by

y =0.02 (m ) \sin \left [ 2\pi \left ( \frac{t}{0.04(s)}-\frac{x}{0.50(m)} \right ) \right ]

The tension in the string is

  • Option 1)

    6.25 N

  • Option 2)

    4.0 N

  • Option 3)

    12.5 N

  • Option 4)

    0.5 N

 

Answers (1)

best_answer

As we learnt in

Speed of wave on string -

v= \sqrt{\frac{T}{\mu }}
 

- wherein

T= Tension in the string

\mu = linear mass density

 

 Given y=0.02(m) sin\left[2\pi \frac{t}{0.04(sec)}-\frac{x}{0.50(m)} \right ]

y=Asin(\omega t-kx) \rightarrow Comparing with standard equation.

V=\sqrt{\frac{T}{mu}}

T=V^{2}\mu

V=\frac{\omega}{K}\ \; \Rightarrow\ \; T=\frac{\omega^{2}}{K^{2}}\mu

Now Put hte value and get the result.

Correct option is 1.

 


Option 1)

6.25 N

This is the correct option.

Option 2)

4.0 N

This is an incorrect option.

Option 3)

12.5 N

This is an incorrect option.

Option 4)

0.5 N

This is an incorrect option.

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