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Numeriprimi
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Homework Statement
The rod of length l and mass m_0 is hinged on two same wires (Fig. 3 on second page - example ,,4. Zvučící dráty" - http://fyzikalniolympiada.cz/archiv/55/fo55a1_z.pdf). With this load, each of the wires gives basic tone height c in natural tuning, f_c = 264 Hz.
A) Move the left wire to the right wire (Fig.4). Now wires sounding in fourth interval: f(left wire)/f(right wire) = 4/3. Determine the length x_1 of move and the frequencies f_1 and f_2.
B) Back to the initial situation - now hing a weight on rod (Fig. 4). Than left wire sounding in tone e a nd right wire sounding in tone g. YOU KNOW: f_e/f_c = 5/4 and f_g/f_c = 3/2. The frequency of tone is proportional to the square root of the tension force.
Determine the length x_2 and the m of weight.
The attempt at a solution
A) Determine the frequencies f_1(left) and f_2(right): 4/3 = f_1/f_2; f_2 is still on c, so f_2 = f_c = 264 Hz; f_1 = 4/3 * f_2 = 4/3 * 264 Hz = 352 Hz
Determine the length x_1 ... I have a strange solution, may wrong.
f_1(left)/f_2(right) = distance of right wire to the left end of the rod / distance of left wire to the right end of rod = l/(l-x_1)=4/3; 3l = 4l - 4x_1; l = 4x_1; x_1 = l/4, so, this is my resoult.
B) We what know what is f_e/f_g... f_e/f_g = f_e/f_c : f_g/f_c = f_e/f_g = 5/4 : 3/2 = 5/6
The frequency of tone is proportional to the square root of the tension force... f= k*√F
f_e/f_g = (k*√F_1)/(k*√F_2) = √(F_1/F_2) = 5/6
F_1/F_2 = 5/6 * 5/6 = 25/36 ... So, this is ratio of the acting forces. I don't know more. Can you help me and check my calculations? Thank you very much and sorry for my bad English :-)
The rod of length l and mass m_0 is hinged on two same wires (Fig. 3 on second page - example ,,4. Zvučící dráty" - http://fyzikalniolympiada.cz/archiv/55/fo55a1_z.pdf). With this load, each of the wires gives basic tone height c in natural tuning, f_c = 264 Hz.
A) Move the left wire to the right wire (Fig.4). Now wires sounding in fourth interval: f(left wire)/f(right wire) = 4/3. Determine the length x_1 of move and the frequencies f_1 and f_2.
B) Back to the initial situation - now hing a weight on rod (Fig. 4). Than left wire sounding in tone e a nd right wire sounding in tone g. YOU KNOW: f_e/f_c = 5/4 and f_g/f_c = 3/2. The frequency of tone is proportional to the square root of the tension force.
Determine the length x_2 and the m of weight.
The attempt at a solution
A) Determine the frequencies f_1(left) and f_2(right): 4/3 = f_1/f_2; f_2 is still on c, so f_2 = f_c = 264 Hz; f_1 = 4/3 * f_2 = 4/3 * 264 Hz = 352 Hz
Determine the length x_1 ... I have a strange solution, may wrong.
f_1(left)/f_2(right) = distance of right wire to the left end of the rod / distance of left wire to the right end of rod = l/(l-x_1)=4/3; 3l = 4l - 4x_1; l = 4x_1; x_1 = l/4, so, this is my resoult.
B) We what know what is f_e/f_g... f_e/f_g = f_e/f_c : f_g/f_c = f_e/f_g = 5/4 : 3/2 = 5/6
The frequency of tone is proportional to the square root of the tension force... f= k*√F
f_e/f_g = (k*√F_1)/(k*√F_2) = √(F_1/F_2) = 5/6
F_1/F_2 = 5/6 * 5/6 = 25/36 ... So, this is ratio of the acting forces. I don't know more. Can you help me and check my calculations? Thank you very much and sorry for my bad English :-)