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~christina~
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[SOLVED] Wave on a wire
A transverse wave on a taut wire has amplitude of 0.200mm and a frequency of 500Hz. It travels with a speed of 196m/s.
a) write an equation in SI units of the form [tex]y(x,t)= Asin( \omega t- kx) [/tex] for this wave
b)The linear mass density of this wire is 4.10g/m Find the Tension in the wire
c) what are the transverse velocity and the acceleration of the wave when x= 19.7m and t= 0.101s
F= -kx
[tex] v= \omega/ k [/tex] ==> teacher gave me this equation but I can't find it in the book...is it valid?
[tex] f= 1/T= \omega/ 2 \pi [/tex]
a)
[tex] f= 1/T= \omega/ 2 \pi [/tex]
[tex]T= 0.002s[/tex]
[tex] v= \omega/ k [/tex]
[tex]2 \pi (500Hz)= \omega [/tex]
[tex] \omega= 3151.59rad/s [/tex]
[tex]k= \omega / v [/tex]
[tex]3141.59rad/s / 196m/s= 16.02[/tex] => I'm not sure it's suppsosed to be that large
I guess I'd just plug in the numbers but I'm not sure if the way I got the numbers is correct.
b) I don't know how to find this
c) I think I would just differentiate the original equaiton with the numbers included and then just plug in the values given and find the numbers.
I have a question though.
Is the transverse velocity always found through the the differential equation?
Thank you very much
Homework Statement
A transverse wave on a taut wire has amplitude of 0.200mm and a frequency of 500Hz. It travels with a speed of 196m/s.
a) write an equation in SI units of the form [tex]y(x,t)= Asin( \omega t- kx) [/tex] for this wave
b)The linear mass density of this wire is 4.10g/m Find the Tension in the wire
c) what are the transverse velocity and the acceleration of the wave when x= 19.7m and t= 0.101s
Homework Equations
F= -kx
[tex] v= \omega/ k [/tex] ==> teacher gave me this equation but I can't find it in the book...is it valid?
[tex] f= 1/T= \omega/ 2 \pi [/tex]
The Attempt at a Solution
a)
[tex] f= 1/T= \omega/ 2 \pi [/tex]
[tex]T= 0.002s[/tex]
[tex] v= \omega/ k [/tex]
[tex]2 \pi (500Hz)= \omega [/tex]
[tex] \omega= 3151.59rad/s [/tex]
[tex]k= \omega / v [/tex]
[tex]3141.59rad/s / 196m/s= 16.02[/tex] => I'm not sure it's suppsosed to be that large
I guess I'd just plug in the numbers but I'm not sure if the way I got the numbers is correct.
b) I don't know how to find this
c) I think I would just differentiate the original equaiton with the numbers included and then just plug in the values given and find the numbers.
I have a question though.
Is the transverse velocity always found through the the differential equation?
Thank you very much