Question In an attempt to get your name in Guinness World Records, youbuild a bass viol with strings of length 5.00 m between fixedpoints. One string, with linear mass density 40.0 g/m, is tuned toa 20.0-Hz fundamental frequency (the lowest frequency that thehuman ear can hear). Calculate (a) the tension of this string, (b)the frequency and wavelength on the string of the second harmonic,and (c) the frequency and wavelength on the string of the secondovertone. Correct Solutions given: (A) 1600 N (B) 40.0 Hz, 5.00m (C) 60.0 Hz, 3.33 m
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In an attempt to get your name in Guinness World Records, you build a bass viol with strings of length 5.00 m between fixed points. One string, with linear mass density 40.0 g/m, is tuned to a 20.0-Hz fundamental frequency (the lowest frequency that the human ear can hear). Calculate (a) the tension of this string, (b) the frequency and wavelength on the string of the second harmonic, and (c) the frequency and wavelength on the string of the second overtone.
Correct Solutions given: (A) 1600 N (B) 40.0 Hz, 5.00 m (C) 60.0 Hz, 3.33 m
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(a)\begin{aligned}V & =f \lambda \\\lambda & =\frac{n l}{2}=\frac{l}{2}=\frac{5}{2}=2.5 \mathrm{~m} \\V & =20(2.5)=50 \mathrm{~m} / \mathrm{s} \\V & =\left(\frac{T}{P}\right)^{0.5} \\2500 & =\frac{T}{40 \times 10^{-3}} \\T & =1600 \mathrm{~N}\end{aligned}(b) \lambda=5 \mathrm{~m} \quad \Rightarrow f_{2}=40 \mathrm{~Hz}(c)\begin{aligned}L & =\frac{3 \lambda}{2} \\\lambda & =\frac{2(5)}{3}=3.33 \mathrm{~m} \\f_{3} & =60 \mathrm{~Hz} .\end{aligned} ...