SOLUTION(A) Find the first three harmonics at the given tension.Calculate the speed of the wave on thewire:Find the wire's fundamental frequency:Find the next two harmonics bymultiplication:=V =f₁Substitute the values of F, μ, and L.F1/280 N(=) ¹/² = (2.00 x 10-³ kg/m=(B) Find the wavelength of the sound waves produced.Solve vsfλ for the wavelength andsubstitute the frequencies.F==AVf₁2L(C) Find the fundamental frequency corresponding to the elastic limit.Calculate the tension in the wire fromthe elastic limit:f₁f₂ = 2f₁ = 2.00 × 10² Hz, ƒ3 = 3ƒ₁ = 3.00 × 10² HzA₁ = v₁/f₁ = (345 m/s)/(1.00 x 10² Hz) = 3.45 m1₂ = vs/f₂ = (345 m/s)/(2.00 x 10² Hz) = 1.73 m^₂ = vs/f3 = (345 m/s)/(3.00 x 10² Hz) = 1.15 m=2.00 × 10² m/s2(1.00 m)elastic limit →→ F = (elastic limit) AF = (2.80 x 108 Pa) (2.56 × 10-7m²) = 71.7 N1V2LF1/2-= 1.00 x 10² Hzμ= 2.00 x 10² m/s12(1.00 m)71.7 N2.00 x 10-³ kg/m= 94.7 Hz PRACTICE ITUse the worked example above to help you solve this problem.(a) Find the frequencies of the fundamental, second, and third harmonics of a steel wire 1.18 mlong with a mass per unit length of 2.40 x 10-³ kg/m and under a tension of 83.9 N.f₁ =Hzf₂ =Hzf3=Hz(b) Find the wavelengths of the sound waves created by the vibrating wire for all three modes.Assume the speed of sound in air is 342 m/s.2₁:^₂ =13 =mmm(c) Suppose the wire is carbon steel with a density of 7.89 × 10³ kg/m³, a cross-sectional area A= 2.68 x 10-7 m², and an elastic limit of 2.50 × 108 Pa. Find the fundamental frequency if the wireis tightened to the elastic limit. Neglect any stretching the wire (which would slightly reduce themass per unit length).Hz

PRACTICE IT : A) Length (L) = 1.18 m mass per unit length (μ) = 2.40×10-3 kg/mTension (T) = 83.9 N…

PRACTICE IT Use the worked example above to help you solve this problem. (a) Find the frequencies of the fundamental, second, and third harmonics of a steel wire 1.18 m long with a mass per unit length of 2.40 x 10-3 kg/m and under a tension of 83.9 N. f₁ = Hz √₂ = Hz f3= Hz (b) Find the wavelengths of the sound waves created by the vibrating wire for all three modes. Assume the speed of sound in air is 342 m/s. A₁ = m d₂ = m A3 = m (c) Suppose the wire is carbon steel with a density of 7.89 x 10³ kg/m³, a cross-sectional area A = 2.68 x 10-7 m², and an elastic limit of 2.50 x 108 Pa. Find the fundamental frequency if the wire is tightened to the elastic limit. Neglect any stretching of the wire (which would slightly reduce the mass per unit length). Hz

PRACTICE IT Use the worked example above to help you solve this problem. (a) Find the frequencies of the fundamental, second, and third harmonics of a steel wire 1.18 m long with a mass per unit length of 2.40 x 10-3 kg/m and under a tension of 83.9 N. f₁ = Hz √₂ = Hz f3= Hz (b) Find the wavelengths of the sound waves created by the vibrating wire for all three modes. Assume the speed of sound in air is 342 m/s. A₁ = m d₂ = m A3 = m (c) Suppose the wire is carbon steel with a density of 7.89 x 10³ kg/m³, a cross-sectional area A = 2.68 x 10-7 m², and an elastic limit of 2.50 x 108 Pa. Find the fundamental frequency if the wire is tightened to the elastic limit. Neglect any stretching of the wire (which would slightly reduce the mass per unit length). Hz

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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