Chapter 14 Overview
13.7 Waves 14.5 Spherical and Plane Waves 13.8 Frequency, Amplitude, and Wavelength 14.6 The Doppler Effect 13.9 The Speed of Waves on 14.7 Interference of Sound Strings Waves 13.10 Interference of Waves 14.8 Standing Waves 13.11 Reflection of Waves 14.9 Forced Vibrations and Resonance 14.1 Producing a Sound Wave 14.10 Standing Waves in Air 14.2 Characteristics of Sound Columns Waves 14.11 Beats 14.3 The Speed of Sound 14.12 Quality of Sound 14.4 Energy and Intensity of Sound Waves
Definitions Definitions
Pulse – one wave bump Amplitude – maximum distance the wave moves above or below the equilibrium point Traveling wave – moving pulse Crest – peak of wave Medium – matter that wave travels through Trough – bottom of wave Transverse wave – particles move perpendicular to wave velocity Wavelength – the desistance from two successive points on a wave (crest to crest) Longitudinal wave – particles of medium move parallel to direction of wave motion Wave speed – speed that a certain part of the wave (crest) Mechanical wave – requires matter (medium) moves through the medium
Equation Speed of a Wave Superposition Principle v = fλ When two or more traveling waves encounter each other while moving through a medium, the resultant wave is found by Where v is wave speed, f is frequency, and λ is wavelength adding together the displacements of the individual waves point by point. Definitions Reflection of Waves
Constructive interference – waves FIXED END (HARD BOUNDARY) FREE END (LOOSE BOUNDARY) that overlap in phase, or crest to crest and trough to trough
Destructive interference – waves that overlap 180° out of phase, or crest to trough and trough to crest
Making Connections The speaker (and the particles of air) acts like mass-spring systems in SHM. Definitions Compression – high molecular density and high air pressure Rarefaction – low density and Similarly, the antinode of a low pressure standing wave acts like a mass- spring system in SHM.
Waves Definitions
Audible – longitudinal waves TRANSVERSE LONGITUDINAL that lie within the range of sensitivity of the human ear, The vibrations of the elements The motion of the elements of approximately 20 to 20,000 Hz of the medium are at right the medium is back and forth angles to the direction of travel along the direction in which the Infrasonic – frequencies below of the wave. wave travels the audible range Ultrasonic – frequencies above the audible range Equations Concept Wave Speed on a String As seen in the previous equation, the tension in the string and v = √(T/μ) type of string is what decides the speed of the wave.
Where v is wave speed, T is tension, and μ is mass of string per This is a common theme for waves. The medium that the wave unit length called linear density (mass/length) travels through is what decided the speed, NOT the frequency or amplitude. Linear Density μ = m/L For waves on a string, another way of talking about the medium is the tension in the string and the linear mass density of the string. Where μ is linear density, m is mass of rope, and L is length of rope If the medium is constant, the speed is constant. SI Unit: kg/m
Equation
Intensity of a Wave Definitions I = P/A Wave fronts – circular arcs that represents lines of maximum intensity Where I is intensity, P is power, and A is area Rays – radial lines pointing outward from the source and perpendicular to wave fronts SI Unit: Watts per Plane waves – wave fronts so meter squared far from the source they are (W/m2) approximately parallel planes
Definitions Superposition principle – two waves combine to form the The Doppler Effect resultant wave Standing wave – wave that appears to stand still but is really The wavelength shortens and the frequency increases (sounds two waves interfering seem higher pitch) when an observer is moving toward the sound source. Node – location of zero net displacement due to destructive interference Antinode – largest amplitude of standing wave due to Or constructive interference Fundamental frequency – lowest possible frequency The wavelength increases and the frequency decreases (sounds First harmonic – another name for fundamental frequency seem lower pitch) when an observer is moving away from the Second harmonic – also called first overtone, is twice the first sound source. harmonic Third harmonic – also called second overtone, is three times the first harmonic Equations Harmonic Series for Standing Waves on a String and Pipe Open at Both Ends
fn = nv/2L
Where f is the frequency, n is the harmonic number, v is the speed of the waven on the string, and L is the length of the string.
Where fn is the frequency, n is the harmonic number, v is the speed of the wave in air, and L is the length of the pipe
Harmonic Series for Standing Waves in Pipe Open at One End
fn = nv/4L
Where fn is the frequency, n is the harmonic number, v is the speed of the wave in air, and L is the length of the pipe. Note: only odd harmonics are allowed
Definitions
Forced vibration – an object is periodically pushed Resonant frequency – natural frequency of the system Resonance – the forced vibration matches the resonant frequency and the amplitude increases timbre – characteristic sound quality
Resonance Definition
If a loud sound is heard for the first harmonic, the length Beats – alternating loudness of air is approximately ¼ of a full wave so you can take L due to two waves of slightly and multiply by four to get an estimate of the different frequencies wavelength. interfering
The number of beats per It is better to find two consecutive loud spots and second you hear is how far off subtract them to find the length of a football (half of a the two frequencies are from wave) and then double that to get full wavelength. each other in Hz.