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physicslab2

# physicslab2 - Lab 2 Oscillations of a String Staci Williams...

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Lab 2: Oscillations of a String Staci Williams Kevin Schesing, Nicole Harty, Caitlin Kubota Section 015 Due February 20, 2010
Theory : 3 Free Oscillations When a string is fixed at both ends it is assumed that it will vibrate in the x-y plane, with the length of the string designated by x, with the string fixed at x=0 and x=L. The transverse displacement of the string is y=y(x,t), and the string has constant tension and a uniform mass per unit length. Newton’s 2 nd Law is applied in the y direction to a length dx of the string without damping this wave equation is used: The solution to the equation is g(x+/-vt), where g is any function and v= T/ , ρ traveling in the positive or negative x direction with speed v. There will be sinusoidal normal mode solutions with the form y = f (x) cos t, where is ω ω the angular frequency and t is the time, with only certain values of satisfy ω boundary solutions Assume f(x) to be in the form of A sin 2 / π λ , where A and are constants and λ the boundary conditions y(l,t)=0 are only satisfied if: Subscript n refers to the normal mode and we can find angular frequencies, by using frequency v in Hz rather than in rad/s, from =2 ω ω v and the π normal frequency modes are:

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Normal mode vibrations are called standing waves and are produced when two sinusoidal waves of the same frequency and amplitude are traveling on the string in opposite directions. Stationary parts are at y= 0 and called nodes are located λ /2 apart. The two fixed ends are nodes, and the lowest frequency/ first mode there are no other nodes, and the next mode will have one more, and the next will have one more than the previous, etc. In lab both the dotted and spotted lines will be seen, with the antinodes being the points of maximum amplitude. The wave relationship λ v= v. For a given T and p, the speeds of the waves are a constant independent of the frequency and wavelength, with waves being dispertionless. 6 Forced Oscillations
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physicslab2 - Lab 2 Oscillations of a String Staci Williams...

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