Wave Motions & Sound

Wave Motions & Sound Chapter 5

An elastic material is one that is capable of recovering its shape after a force deforms it 3 considerations The greater the applied force, the greater the compression or stretch (deformation) of the spring from its original shape The spring appears to have an internal restoring force, which returns it to its original shape The farther the spring is pushed or pulled, the stronger the restoring force that returns the spring to its original shape Hooke’s Law: F = -kx A pulse is one back and forth motion A vibration is a pulse that repeats itself Almost any solid can be made to vibrate if it is elastic Simple example of a mass hanging on a spring Another example is the simple pendulum Such periodic motion is called simple harmonic motion (SHM) The motion will continue for a while, slowly decreasing due to air resistance and internal friction If these were eliminated, the vibrations would continue undiminished forever Forces & Elastic Materials

Descriptive terms Amplitude The extent of displacement from the equilibrium position Cycle (oscillation) A complete pulse Period The number of seconds to make a complete pulse Frequency The number of oscillations per second Hertz (Hz) is the unit of frequency Waves are usually periodic, repetitive vibrations. Pulses are short duration disturbances Both pulses and periodic vibrations can produce a physical wave that travels through its surroundings 2 basic types of waves Transverse waves Disturbance is perpendicular to the direction of wave travel Longitudinal waves Disturbance is parallel to the direction of wave travel Ex: What type of wave is “the wave” at a football game? Ex: What type of wave is sound? Vibrations

Describing waves Graphical representation • Pure harmonic waves = sines or cosines Wave terminology • Wavelength • Amplitude • Frequency • Period Wave propagation speed

Require medium for transmission Speed varies with Inertia of molecules Interaction strength Temperature Various speeds of sound Sound waves

Longitudinal mechanical waves can travel through solids, liquids, or gases Transverse mechanical waves can only travel through solids, but not through fluids (gases and liquids) Since sound can travel through air (a gas), what kind of wave must it be? A sound wave is a longitudinal pressure wave, and the disturbance is slight variations of air pressure We speak of the (very tiny) regions of increased pressure as condensations, and the regions of decreased pressure as rarefactions The variations in pressure set up corresponding vibrations in the eardrum, which in turn causes vibrations in the tiny bones of the ear (malleus, incus, and stapes) These vibrations are converted into nerve signals and sent to the brain along the auditory nerve Waves in Air

A tuning fork produces a single frequency of sound (a pure tone) Most sounds are a combination of many frequencies Musical notes are combinations of tones with certain frequency ratios that sound pleasing to our ear Noise is a random or chaotic combination of frequencies that is unpleasant The normal range of the human ear is from 20 Hz to 20 kHz (20 – 20,000 Hz). Sounds with frequency above 20 kHz are called ultrasonic Dogs, cats, rats, and bats can hear in the ultrasonic frequency range Ultrasonic medical images are used to image babies in their mothers’ wombs in preference to potentially harmful X-rays Waves in Air

Wavelength is the distance between successive crests of a traveling wave Wavelength is measured in meters or portions of a meter just like any other length We often define waves by their wavelength, especially lightwaves The wave equation relates the speed of a wave with its wavelength and its frequency v = f where  is the wavelength and f is the frequency For a wave such as a sound wave, with fixed speed, as the frequency increases, the wavelength decreases Waves in Air

Sound is a longitudinal mechanical wave Because it is a mechanical wave, it requires a medium through which to travel The longitudinal waves can travel through gases, liquids, or solids, but cannot travel through the vacuum of space Movies which include sound effects for objects (like rockets) traveling through space are not realistic The speed of sound depends on the type of material in which it is traveling and the temperature Sound travels through air at about 340 m/s, but travels through steel at 5,940 m/s The warmer the air temperature, the faster the speed of sound Sound waves

Velocity of sound in air • Varies with temperature • Greater kinetic energy -> sound impulse transmitted faster • Increase factor (units!): 0.6 m/s/°C; 2.0 ft/s/°C

Reflection When waves strike a surface, they may be absorbed, transmitted, or reflected (or some combination of these) Reflection is to be bounced off the surface Law of reflection is that the angle of the reflected wave is equal to the angle of the incident wave (measured relative to the normal of the surface) When sound is reflected from smooth, hard surfaces, the waves can be reflected many times, causing reverberation Rooms (lecture halls, auditoriums, etc) need to be designed with an adequate amount of reverberation to avoid being acoustically “dead” Refraction Refraction is the bending of a wave front as it passes through a boundary surface Occurs when the speed on one side of the boundary is different than the speed on the other side of the boundary The direction of the wave’s travel is changed One example of this is when there are different temperature layers in the air. On calm, clear night, air near the surface may be several degrees cooler than air at rooftop height. Sound will be refracted toward the ground, and you can hear sounds from much farther away than usual Waves

Reflection • Wave rebounding off boundary surface • Reverberation - sound enhancement from mixing of original and reflected sound waves • Echo • Can be distinguished by human ear if time delay between original and reflected sound is greater then 0.1 s • Used in sonar and ultrasonic imaging

When two or more waves meet, they can pass through each other without reflecting or refracting However, at the place where they meet the waves interfere with each other to produce a new wave disturbance The new wave will have a different amplitude, which is the algebraic sum of the amplitudes of the two separate wave patterns This sum depends upon the relative phase of the two waves If the waves are in phase, the amplitudes reinforce each other, making a larger amplitude. This is constructive interference If the waves are out of phase, the amplitudes cancel each other, making a smaller resulting amplitude. This is destructive interference If two sources have different frequencies, when they interfere the pattern of constructive and destructive changes with time Then you will have time of large amplitude followed by time of very small amplitude We call the resulting effect “beats” The number of beats per second is merely the difference between the frequencies of the two sources Interference

Interference, cont. • Two or more waves combine • Constructive interference • Peaks aligned with peaks; troughs aligned with troughs • Total wave enhanced

Interference, cont. • Destructive interference • Peaks aligned with troughs • Cancellation leads to diminished wave • Beats • Overall modulation of sound from mixing of two frequencies • Beat frequency = difference in two frequencies

How loud is that sound? • Subjective perception related to • Energy of vibrating object • Atmospheric conditions • Distance from source • Intensity range of human hearing (decreases with age!)

Better reflects nonlinear relationship between perceived loudness and intensity Logarithmic scale yields simpler numbers Decibel scale

Resonance • Excitation of natural frequency (“resonant frequency”) by a matching external driving frequency • Examples • Pushing a swing • Tuned boxes and tuning forks • Earthquake resistant architecture • It is possible for external waves to enhance a resonant frequency so much that the object destroys itself • Wine goblet • Tacoma Narrows Bridge

Doppler Shift • In the early 1800s, Austrian scientist Christian Doppler noticed that the pitch of sound was affected by the speed of its source • Put a trumpet player on a train – as he approaches, the pitch is higher than when he recedes (assuming that he plays the same note the whole time) • Relative motion of source and detector cause a variation in the frequency of the wave • We use this effect in many different ways • Doppler weather radar • Traffic radar (speed detection) • Red shift of light in astronomy • It is true for all kinds of waves Doppler Simulation

Wave Motions & Sound