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A wave on a string is described by D(x,t)= (2.00cm)sin[(12.57rad/m)x−(638rad/s)t], where x is in m and t is in s. The linear density of the string is 5.00g/m.


What is the string tension?

What is the maximum displacement of a point on the string?

What is the maximum speed of a point on the string?

Answer :

Answer : The string tension is [tex]T = 12.882 N[/tex]

The maximum displacement is 0.02 m

The maximum speed is [tex]v = 12.76\ m/s[/tex]

Explanation :

Given that,

D(x,t) = (2.00 cm) sin [(12.57rad/m)x - (638rad/s)t]

Where, x is in m and t is in sec.

Linear density of the string = 5.00 g/m

We know that,

Velocity of the wave

[tex]v = \dfrac{\omega}{k}[/tex]

[tex]v = \dfrac{638}{12.57}\ m/s[/tex]

[tex]v = 50.76\ m/s[/tex]

Now, the string tension

[tex]v = \sqrt\dfrac{T}{m}[/tex]

[tex]T = 0.005\times (50.76)^{2}\ N[/tex]

[tex]T = 12.882 N[/tex]

The maximum displacement is 0.02 m

The maximum speed  

[tex]v = a \omega[/tex]

[tex]v = 0.02\times638\ m/s[/tex]

[tex]v = 12.76\ m/s[/tex]

Hence, this is the required solution.





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