When a transverse wave travels down a real wire there are forces acting on each portion of the wire in addition to the force resulting from the tension in the wire. An equation that gives an improved description of a wave on a real wire is 8²y Ət² = T (0²y) əx² - ay where T> 0 is the tension, μ> 0 is the mass per unit length and a > 0 is a constant. (a) Find the relationship between w, T, μ, k, a for y(x, t) = A cos(wt - kx) to be a solution where w> 0 and k ≥0 are constants. (b) What is the lowest angular frequency that the wire can support according to the condition found in the previous question.
When a transverse wave travels down a real wire there are forces acting on each portion of the wire in addition to the force resulting from the tension in the wire. An equation that gives an improved description of a wave on a real wire is 8²y Ət² = T (0²y) əx² - ay where T> 0 is the tension, μ> 0 is the mass per unit length and a > 0 is a constant. (a) Find the relationship between w, T, μ, k, a for y(x, t) = A cos(wt - kx) to be a solution where w> 0 and k ≥0 are constants. (b) What is the lowest angular frequency that the wire can support according to the condition found in the previous question.
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Transcribed Image Text:When a transverse wave travels down a real wire there are forces acting on each
portion of the wire in addition to the force resulting from the tension in the wire.
An equation that gives an improved description of a wave on a real wire is
a² y
Ət²
=
T
μl
(8
(8²y
?x2
- ay
-
where T > 0 is the tension, µ > 0 is the mass per unit length and a > 0 is a
constant.
(a) Find the relationship between w, T, u, k, a for y(x, t) = A cos(wt - kx) to be a
solution where w> 0 and k ≥ 0 are constants.
(b) What is the lowest angular frequency that the wire can support according to the
condition found in the previous question.
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