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The transverse displacement of a string ...

The transverse displacement of a string is given by `y ( x , t ) = 0.06 sin ((2pi)/(3)) x cos ( 120 pi t)` where 'x' & 'y' are 'm' and 't' is s. The length of the string is 1.5m and its mass is `3.0 xx 10^(-2) kg`.
Determine the tension in the string.

Text Solution

Verified by Experts

The given equation is,
`y( x,t) =0.06 sin ((2pi)/(3))x cos(120pit)`comparing this with
We know that, `v =sqrt((T)/( mu ))`
i.e., ` T = v^(2) mu `
where `mu =( M)/( L) = ( 3 xx 10^(-2))/(1.5) = 2 xx 10^(-2) kgm^(-1)`
Hence `T = 180 xx180 xx 2 xx10^(-2) N`
T = 64.8 N
`T = 6.48 xx 10^(2) N`
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The transverse displacement of a string is given by y ( x , t ) = 0.06 sin ((2pi)/(3)) x cos ( 120 pi t) where 'x' & 'y' are 'm' and 't' is s. The length of the string is 1.5m and its mass is 3.0 xx 10^(-2) kg . Does the function represent a travelling wave or stationary wave ?

The transverse displacement of a string is given by y ( x , t ) = 0.06 sin ((2pi)/(3)) x cos ( 120 pi t) where 'x' & 'y' are 'm' and 't' is s. The length of the string is 1.5m and its mass is 3.0 xx 10^(-2) kg . Interpret the wave as a superposition of two waves travelling in opposite direction. What is the wavelength, frequency and speed of each wave?

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