(a) Find the frequencies of the fundamental, second, and third harmonics of a st

Question

(a) Find the frequencies of the fundamental, second, and third harmonics of a steel wire 1.17 m long with a mass per unit length of 2.50 × 10-3 kg/m and under a tension of 76.0 N 102 Your response differs from the correct answer by more than 10%. Double check your calculations. Hz 204 Your response differs from the correct answer by more than 10%. Double check your calculations. Hz 306 our response differs from the correct answer by more than 10%. Double check your calculations. Hz f2 f3 (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 340 m/s 3.27 Your response differs from the correct answer by more than 10%. Double check your calculations. m 1.67 Your response differs from the correct answer by more than 10%. Double check your calculations. m 1.11 Your response differs from the correct answer by more than 10%. Double check your calculations. m (c) Suppose the wire is carbon steel with a density of 7.64 x 103 kg/m3, a cross-sectional area A = 2.70 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)

Explanation / Answer

here,

(a)

mass per unit length , u = 0.0025 kg/m

tension , t = 76 N

length of wire , l = 1.17 m

fundamental frequency , f1 = 1/(2*l) * sqrt(T/u)

f1 = 1/( 2 * 1.17) * sqrt(76/0.0025)

f1 = 74.51 Hz

seccond harmonic frequency , f2 = 2 * f1 = 149.02 Hz

third harmonic frequency , f3 = 3 * f1

f3 = 223.53 Hz

(b)

speed of sound , c = 340 m/s

lamda1 = c/f1

lamda1 = 4.56 m

lamda2 = c/f2

lamda2 = 2.28 m

lamda3 = c/f3

lamda3 = 1.52 m

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