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CHurst5841
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The problem is as follows:
"A string exhibits standing waves with 4 antinodes when a mass of 200 g is hanging over the pulley (see attached figure). What mass will produce a standing wave pattern with 6 antinodes?"
The equations that I have found in the relevant section of the text are as follows:
v=\sqrt{\frac{T}{\mu}}
v=f\lambda
f=\frac{1}{\lambda}\sqrt{\frac{T}{\mu}}
T=mg
\frac{1}{n}=\frac{1}{Lf}\sqrt{\frac{T}{\mu}}=[\frac{1}{Lf}\sqrt{\frac{g}{\mu}}}]\sqrt{m}
Where...
T = tension in the spring as supplied by the weight of the hanging mass
mu = linear density of the string
lambda = wavelength
f = frequency of oscillation
m = mass suspended from spring
g = gravitational constant
L = length of the string
I've attached the diagram referenced above for further illustration.
http://img180.imageshack.us/img180/3735/sc002c9a37ww1.th.jpg
I have no idea where to even begin with the problem given the lack of information provided by the question.
Please help!
"A string exhibits standing waves with 4 antinodes when a mass of 200 g is hanging over the pulley (see attached figure). What mass will produce a standing wave pattern with 6 antinodes?"
The equations that I have found in the relevant section of the text are as follows:
v=\sqrt{\frac{T}{\mu}}
v=f\lambda
f=\frac{1}{\lambda}\sqrt{\frac{T}{\mu}}
T=mg
\frac{1}{n}=\frac{1}{Lf}\sqrt{\frac{T}{\mu}}=[\frac{1}{Lf}\sqrt{\frac{g}{\mu}}}]\sqrt{m}
Where...
T = tension in the spring as supplied by the weight of the hanging mass
mu = linear density of the string
lambda = wavelength
f = frequency of oscillation
m = mass suspended from spring
g = gravitational constant
L = length of the string
I've attached the diagram referenced above for further illustration.
http://img180.imageshack.us/img180/3735/sc002c9a37ww1.th.jpg
I have no idea where to even begin with the problem given the lack of information provided by the question.
Please help!
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