1) Do the resonance frequencies depend on the tension of the string? 2) Do the r
ID: 2204901 • Letter: 1
Question
1) Do the resonance frequencies depend on the tension of the string? 2) Do the resonance frequencies depend on the line mass density of the string? 3) Do the resonance frequencies depend on the length of the string? 4) A string of mass 0.0003 kg/m and 0.5 m long is vibrating 200 cycles per second. What must be the tension? What hanging mass would produce this tension? 5) Two strings equal in length and made of the same material are subjected to tensions in proportion of 1 to 4; the one under the greater tension is the thicker string. If they vibrate at the same frequency, how do their diameters compare?Explanation / Answer
freq string under tension (f) = (1/k*L)v(T/m) --------------------------- k is constant depending as to how it vibrates, plucked etc k =2 for fundamental freq ----------------------- m = mass/length = linear mass density T = tension (N), L = length ============= 1) yes, 2) yes, 3) yes[for 2 wires, 1m and 2m density is same but greater L will allow lower freq. --------------- m = mass/L = pi(D/2)^2 L / L = pi(D/2)^2 = 0.25 pi D^2 4) (f1) = (1/k*L)vT/(0.25pi D-thin^2) (f2) = (1/k*L)v4T/(0.25pi D-thick^2) ----------------------------- f2/f1 = v(4T/(0.25pi D-thick^2) v(0.25pi D-thin^2)/T f2/f1 = v(4D-thin^2 /(D-thick^2) 2 [D-thin /D-thick] = f2/ f1 = 1 given f1 =f2 D-thick = 2 D-thin
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