Chapter 14 Sound

Sound is a pressure wave caused by vibrating sources. The pressure in the medium carrying the sound wave increases and decreases as the molecules compress and spread. Because sound is a pressure wave that propagates due to molecular movement, it travels faster in more dense materials.

Sound Waves The loudspeaker to the right causes molecules in the air to compress and spread out. The resulting pressure wave is a sound wave. The wave is made of compressions and rarefactions.

Sound Characteristics Sound is a longitudinal wave. Sound is a mechanical wave – it cannot travel in a vacuum. In air at STP, sound travels at 343 m/s

Sound Characteristics Pitch refers to the frequency of the sound wave. Higher pitch means higher frequency. Loudness refers to the amplitude of the sound wave. Louder sounds have larger compressions and carry more energy.

The Human Ear Is sensitive to frequencies ranging from 20 Hz to 20,000 Hz. Infrasonic frequencies are lower than 20 Hz, Ultrasonic frequencies are higher than 20K Hz. The eardrum picks up sound waves and begins to vibrate. The vibrations are carried from the eardrum by the tiny bones in the ear to the inner ear. The vibrations are then picked up by the auditory nerves.

Uses of Sound Waves Echos are created when sound waves are reflected off of a surface. Ultrasound (ultra-sonic means above 20 KHz) uses reflected sound waves to create an image inside the body. Sonar devices also used the ultra-sonic range to create maps of ocean floor and to detect underwater objects. Bats use echolocation to navigate.

Speed of Sound Sound travels at approximately 343 m/s in air at STP, but the speed depends on temperature. v = T c gives the speed of sound in air as a function of temperature

Speed of Sound

Sound Intensity Intensity is a measure of Power/Area and is measured in units of [Watts/m 2 ] The human ear is sensitive to a wide range of intensities (an exponential range) The decibel scale (dB) is a logarithmic scale which linearizes sound intensities.

Intensities that can be detected by the human ear increase exponentially. A logarithmic scale linearizes the exponential values. dB = 10log(I/I 0 )

Examples: Read and copy examples 14.4 and 14.5 into your notes. They are found on pages 478 – 479.

Constructive Interference When two waves from the same source combine, they will combine constructively if the difference in pathlength, ΔL, is an integral number of wavelengths. ΔL = nλ

Constructive Interference If wave forms align, they add constructively.

Destructive Interference When two waves from the same source combine, they will combine destructively if the difference in pathlength is an integral number of half wavelengths. ΔL = nλ/2

Destructive Interference

Example At an open air concert on a hot day (25 degrees Celsius), you sit 7.0 meters and 9.10 meters respectively from a pair of speakers, one at each side of the stage. A musician warming up plays a single 494 Hz tone. What do you hear in terms of intensity?

Beats When two pure tones are nearly the same frequency, beats can be heard as the frequencies combine constructively and destructively. Beat frequency is the difference between the larger frequency and the smaller.

Beats

Beat Frequency When two very similar pitches (frequencies) are sounded, beats will be heard. The beat frequency is found by subtracting the frequency values f b = f 2 – f 1

Doppler Effect The doppler effect is the apparent change in frequency of a source that is moving with respect to an observer. If the source moves towards the observer, the frequency seems to increase. If the source moves away from the observer, the frequency seems to decrease.

Formula for Doppler Effect f o = f s f o gives observed frequency f s gives source frequency v gives speed of sound v s gives speed of source - for source moving towards observer + for source moving away from observer

Example As a truck traveling at 96 km/hour approaches and passes a person standing along the highway, it sounds the horn. The horn has frequency of 400 Hz. What are the frequencies heard by the person as the truck approaches and after it passes?

Musical Instruments Musical instruments produce amplified tones by creating resonance. A cavity (guitar body, drum body, hollow tube) is made to resonate at a particular frequency Wind instruments are made of open or closed pipes (hollow tubes). The length of the tube can be changed using holes or slides. Standing waves are set up inside the cavity to produce resonance.

String Instruments For a stretched string which is fixed at both ends, from Chapter 13: f n = n(v/2L) (using standing waves and v = fλ) v = (F T /µ) 1/2

Closed Pipe Resonator Closed pipes are open at one end and closed at the other (antinode and node) The lowest frequency which resonates is such that L = λ/4; λ= 4L Higher overtones occur at L = 3(λ/4); λ = 4L/3 L = 5(λ/4); λ = 4L/5 L = 7(λ/4)….

Open Pipe Resonator Open pipes are open at each end (antinode at each end). The lowest frequency that resonates is such that L = λ/2; λ = 2L The higher overtones are such that L = 2(λ/2); λ=(2L)/2 L = 3(λ//2); λ = (2L)/3

Summary for Resonators Closed pipe: λ = 4L, (4L)/3, (4L)/5, … Harmonicsf n = f 1, 3f 1, 5f 1,… Open pipe: λ = 2L, (2L)/2, ((2L)/3,… Harmonics f n = f 1, 2f 1, 3f 1,…

Example An open organ pipe has a length of m. Taking the speed of sound in air to be v = 345 m/s, what is the fundamental frequency of the pipe? What is the first overtone?

Example Consider the human ear to be a cylindrical tube of length 2.54 cm. What would be the lowest resonant frequency? Assume the temperature in the ear canal to be 37 degrees Celsius.