(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
Properties of sound
A sound wave is a mechanical wave (or mechanical vibration) that transit through media such as gas (air), liquid (water), and solid (wood).
Quality Of Sound
A sound or a sound wave is defined as the energy produced due to the vibrations of particles in a medium. When any medium produces a disturbance or vibrations, it causes a movement in the air particles which produces sound waves. Molecules in the air vibrate about a certain average position and create compressions and rarefactions. This is called pitch which is defined as the frequency of sound. The frequency is defined as the number of oscillations in pressure per second.
Categories of Sound Wave
People perceive sound in different ways, like a medico student takes sound as vibration produced by objects reaching the human eardrum. A physicist perceives sound as vibration produced by an object, which produces disturbances in nearby air molecules that travel further. Both of them describe it as vibration generated by an object, the difference is one talks about how it is received and other deals with how it travels and propagates across various mediums.
![(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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F22c6353d-d3c6-4309-95ca-4c63c678b288%2F714c662c-bfe9-4d6e-ae31-423462852290%2Fc7qzrhs_processed.jpeg&w=3840&q=75)
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