(a) Find the frequencies of the fundamental, second, and third harmonics of a steel wire 1.25 m long with a mass per unit length of 2.10 x 10-3 kg/m and under a tension of 83.3 N. f₁ = Hz f₂ = 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 349 m/s. A₁ = m λ₂ m d3 = m (c) Suppose the wire is carbon steel with a density of 7.65 x 103 kg/m³, a cross-sectional area A = 2.53 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

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(a) Find the frequencies of the fundamental, second, and third harmonics of a steel wire 1.25 m
long with a mass per unit length of 2.10 x 10-3 kg/m and under a tension of 83.3 N.
Hz
Hz
f₂ =
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 349 m/s.
A₁ =
m
d₂ =
m
d3 =
m
(c) Suppose the wire is carbon steel with a density of 7.65 x 103 kg/m3, a cross-sectional area A
= 2.53 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
EXERCISE
HINTS: GETTING STARTED I I'M STUCK!
(a) Find the fundamental frequency and second harmonic if the tension in the wire is increased to 116 N.
(Assume the wire doesn't stretch or break.)
ffundamental =
Hz
f2nd harmonic=
Hz
(b) Using a sound speed of 349 m/s, find the wavelengths of the sound waves produced.
λ (larger)
=
m
λ (smaller) =
m
Transcribed Image Text:(a) Find the frequencies of the fundamental, second, and third harmonics of a steel wire 1.25 m long with a mass per unit length of 2.10 x 10-3 kg/m and under a tension of 83.3 N. Hz Hz f₂ = 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 349 m/s. A₁ = m d₂ = m d3 = m (c) Suppose the wire is carbon steel with a density of 7.65 x 103 kg/m3, a cross-sectional area A = 2.53 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 EXERCISE HINTS: GETTING STARTED I I'M STUCK! (a) Find the fundamental frequency and second harmonic if the tension in the wire is increased to 116 N. (Assume the wire doesn't stretch or break.) ffundamental = Hz f2nd harmonic= Hz (b) Using a sound speed of 349 m/s, find the wavelengths of the sound waves produced. λ (larger) = m λ (smaller) = m
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