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6. A transverse periodic wave on a string with a linear density of 0.200 kg/m is described by the following equation: y = 0.08 sin(469t – 28.0x), where x and y are in meters and t is in seconds. What is the tension in the string? A) 3.99 N B) 32.5 N C) 56.1 N D) 65.8 N

Sagot :

Answer:

T = 56.11 N

Explanation:

Given that,

The equation of a wave is :

y = 0.08 sin(469t – 28.0x),

where x and y are in meters and t is in seconds

The linear mass density of the wave = 0.2 kg/m

The speed of wave is given by :

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

Also,

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

We have,

[tex]k=469\ and\ \omega=28[/tex]

Put all the values,

[tex]\dfrac{\omega}{k}=\sqrt{\dfrac{T}{\mu}}\\\\(\dfrac{\omega}{k})^2=\dfrac{T}{\mu}\\\\T=(\dfrac{\omega}{k})^2\times \mu[/tex]

Put all the values,

[tex]T=(\dfrac{469}{28})^2\times 0.2\\\\T=56.11\ N[/tex]

So, the tension in the string is 56.11 N.