Chapter 18 Waves and Sound

Objectives 18.1 Sketch a transverse wave and identify its characteristics 18.1 Discuss the relationship between the frequency and wavelength in a transverse wave 18.1 Using the relationship among wavelength, frequency, and velocity, find one variable when two are given.

Objectives 18.2 Describe the transmission of sound through medium 18.2 Recognize the relationships between intensity and loudness and frequency and pitch 18.2 Illustrate the Doppler effect with a practical example

Objectives 18.3 Explain how sound waves can be used to create images of organs inside the body 18.3 Describe some of the uses of ultrasound technology in medicine 18.4 Distinguish between music and noise 18.4 Describe why different instruments produce sounds of different quality 18.4 Explain two types of wave interference

What is a Wave? How would you define what a “wave” is?

Waves Transfer energy without transferring material Some types of waves transfer energy through material, others transfer energy without needing material Sound waves  Need a medium Light waves  Don’t need a medium

Types of Waves Transverse waves: the motion of the particles is perpendicular to the wave motion. Longitudinal waves: the motion of the particles is parallel to the wave motion.

Transverse Wave moves to side, matter moves up and down

Compression: Matter moves in same direction as wave

Terms of Waves Period: How long it takes to go from crest to crest (back to start) Crests: The high points of a wave (compression in longitudinal) Troughs: The low points (rarefaction in longitudinal)

Terms of Waves Midpoint: The “Home position,” the middle of the wave Amplitude: Distance from midpoint to crest (or trough) Wavelength: Length of wave, generally measured from one crest to another Frequency: How many times a second a wave goes through a cycle

Random Knowledge AM radio waves are broadcast in kilohertz (960 AM is 960 kHz or 960,000 Hz) FM radio waves are broadcast in megahertz (so 100.7 FM is 100.7 MHz or 100,700,000 Hz) Bumblebees flap at 130 Hz Honeybees about 225 Hz Mosquitos about 600 Hz (or 0 Hz after you squash it)

Wave Equation Velocity of the wave is equal to the wavelength times the frequency of the wave A wave is generated in a wave pool. The wavelength is 3.2 m and the frequency is 0.60 Hz. What is the speed of the wave?

Wave Equation The speed of sound is 340 m/s at room temperature. Calculate the wavelength for the following notes Middle range pitch: 256 Hz Low range pitch: 128 Hz High range pitch: 512 Hz

Earthquakes

Types of Waves S- Waves are transverse waves and are not transmitted through fluids. P- Waves are longitudinal waves and can be transmitted through fluids S-Waves travel slower than P-Waves. Geologists are able to pinpoint the epicenter by recording when the waves arrive (P waves travel 4-8 km/s and S waves 2-5 km/s)

Richter Scale The Richter Scale is logarithmic. An earthquake of 3.0 is 10x stronger (more powerful than a 2.0 earthquake and 100x a 1.0 earthquake.

Question How much more energy (by ratio) is released by a 7.2 earthquake on the Richter scale than a 4.2? How much more energy (by ratio) is released by a 8.0 earthquake compared to 4.0?

Intensity of Waves As you get farther away from the source of the wave, the intensity drops because of energy absorbed by the medium being traveled through and mostly because the wave spreads out. Air does not absorb much energy from sound waves so they can be heard from great distances.

As the distance from the sound increases, the arc length of the angle increases 1 / d squared Double distance = ¼ intensity

Sound Waves Sound Waves Areas of compression and rarefaction. Audible range for humans is 20 Hz to 20 kHz. Infrasound refers to waves below 20 Hz and ultrasound refers to waves above 20 kHz.

Decibel Scale The decibel scale is a log rhythmic scale. The lowest intensity of sound that the human ear can hear is the threshold of hearing. The value is 1E-12 W/m2. 0 dBels is 1E-12 W/m2. The equation to figure out how many decibels loud something is

The Human Ear

The Human Ear Pinna = Funnel, collecting waves at opening of Auditory canal (ear canal) Resonance occurs in the ear canal to boost the ear’s sensitivity to sound frequencies between 2 and 5 kHz (this helps us understand speech)

The Human Ear Tympanic membrane = Vibrates in response to the sound waves reaching it. This vibration is transmitted through tiny bones (three of them, called the Auditory ossicles) to the Cochlea The ossicles act as levers, and have a mechanical advantage to amplify the sound waves for the cochlea. (The hammer)

The Human Ear Cochlea = Spiral shaped organ filled with fluid. The pounding of the ossicles on the cochlea produce a compressional wave (longitudinal) which goes through the cochlea. This wave collides with the basilar membrane (not shown on diagram), which functions much like the eyes do in focusing. Based off of the frequency of the waves, it tightens or relaxes to vibrate at its maximum resonance.

The Human Ear On this membrane are the organs of corti. There are a whole bunch of tiny hair cells which bend in response to waves. The bending of the hair cells causes neurons to send electrical signals to the brain.

The Human Ear Other Interesting information: When exposed to loud noises, the muscles which hold the hammer will tighten and pull the hammer away from the drum and make our ears less sensitive to noise. The sound waves which reach the ears are often complex, composed of many frequencies. Our brain does some quick mental math to break the frequency down to its individual frequencies (your brain is smarter than a calculator)

Timbre Timbre A tuning fork produces one single frequency. However, most instruments and our voices produce a complex sound, with many frequencies overlapping on one another. Why does a middle C on an Oboe sound different than middle C on a Trumpet? Timbre.

Timbre The lowest frequency of a sound wave is called the fundamental. The rest of the frequencies are overtones All overtones are integral multiples of the fundamental: ie If the fundamental is 30 Hz, the overtones could be 60, 90, and 120 Hz but could not be 40, 50, or 70 Even if the fundamental is not being produced, our ear “hears” the fundamental and makes the fundamental itself.

Loudness While related to intensity, it also depends on frequency, as our ears hear different frequencies better than others. Our ears hear best between 3-4 kHz. Take note, a person with no hearing loss and excellent hearing cannot hear below the bottom line.

120 0 dB 0 Hz 2-4000 Hz 20k Hz

Pitch Our perception of frequency. Our sense of pitch and frequency is logarithmic, just as loudness is logarithmic with intensity. If you were to play a piano from the lowest note (27.5 Hz) to the highest note (4,190 Hz) you hear equal steps of pitch, but the steps are not equal. The frequency of each note is 5.95% higher than the previous note.

Localization How the ear localizes sound:  Head shadow: Noise is more intense on side of noise as our head is a shadow  Shape of pinna: Faces front, helps with back-front localization  For low frequency sounds, phase difference between the waves helps in localization

Beats When two frequencies are close to one another (< 15 Hz), the waves produce a pulsation called beats. The frequencies are so close that the superposition seems to produce many amplitudes Like turn signal blinkers

Beats The waves do not stay in phase forever, and the wave with a higher frequency gets ahead of the lower frequency one. When they are 180 degrees out of phase, destructive interference occurs, and in phase, constructive. At frequency differences greater than 15 Hz, we hear separate tones.

Standing Waves, Nodes, Antinodes and Interference While matter can not exist in the same space and time as other matter (Two rocks can not exist in the same place), waves can and do (right now our bodies have bazillions of waves passing through them). If you drop two rocks in a pond, the waves can overlap and form an interference pattern. The wave effects are increased, decreased, or even neutralized.

Types of Interference When a crest hits another crest, they add together and increase amplitude. This is called constructive interference. When a crest hits a trough, the waves are cancelled out, the crest “fills in” the trough. This is called Destructive interference.

Destructive Interference Phase Shift Constructive Interference High Pressure Waves can be out of phase. This essentially means that one lags slightly behind another. This can cause varying amounts of interference. High and low pressure areas from both waves match up causing a maximum amount of constructive interference Sound wave with high and low pressures. High pressures line up with the low pressures of a second wave, causing destructive interference. Low Pressure

Out of Phase (180 degrees)

In Phase

Doppler Shift

How things work Police radar is able to tell our speed by doing calculations of frequency. The antenna of the police car sends out a signal (with a certain frequency). Then when the wave gets reflected back, it has a frequency shift based off of how fast the car was moving. That is how radar works.

Question A fire truck turns on its sirens and starts driving at 20 m/s. The siren produces a sound with a frequency of 100 Hz. What is the perceived frequency of an observer (standing still) when: a) The fire truck is approaching? b) The fire truck has moved past? Speed of Sound: 340 m/s

Shock Waves Sonic Boom When an object (usually planes) flies faster than the speed of sound, the crests pile up and produce a cone shaped shock wave. There are two shock waves, one at the front of the object, one at the back of the object.

Sonic Boom It produces an “N” shaped wave, called this because of the N shaped graph of pressure. Initially, the pressure builds up at the front, at the nose of the plane, where all the molecules are crunched together. Then it decreases linearly across the plane, and finally jumps back up as the molecules fly back to fill the hole left by the plane.

Sonic Boom

Under Pressure The pressure change is not very large at all, just 50 – 500 Pascals. The danger and damage is caused by how fast this occurs. For military planes, this change occurs in 0.1 s or less and for the space shuttle in about 0.5 s. Due to the small interval, only one sonic boom is heard from small military fighters, but two can be heard by the space shuttle. The pressure changes can even cause physical damage to buildings.

Mach Speed Mach Rate of the speed of the plane to the speed of sound. A plane flying at Mach 3.3 is flying at a speed of 1,100 m/s compared to the speed of air (3.3 x 331 m/s)

Plane at Mach 0.75

Plane at Mach = 1

Plane at Mach > 1

Plane > Speed of Sound

Sound leaving rifle

Echolocation Echolocation Many animals rely on waves to detect their surroundings. Bats, dolphins, whales, and even some birds find their way around using waves. The emit their own wave and then listen for the echo.

Animal Knowledge Bats and Dolphins when hunting also take advantage of the Doppler effect to determine the speed of the object. Some bats can detect frequency changes as small as 0.1 Hz.

Animal Knowledge Prey fight back as well. Moths (as well as some other prey) can also detect these emitted waves. Upon hearing the waves, they drop to the ground and collapse their wings (to minimize their surface area). Also moths tend to be slightly furry, this helps absorb some of the energy of the wave and reflect the wave back at smaller intensities.

And More Animal Knowledge The tiger moth sends out its own wave that mixes with the bats waves and makes the wave more incoherent to the bat.

Sonar/Echolocation

Sonar Sonar Used to detect how far away the ocean bottom is. Also for detecting enemy vessels and distance away. Question: If the speed of sound in the ocean is 1500 m/s and it takes 0.24 seconds for a sound wave emitted by the boat to return, how far away is the bottom?

Usefulness of Waves Cameras Auto focusing cameras send out a wave to see how far the object is away, and adjust appropriately (not all do this, but some do) Radar: Relies on reflected waves to see the location of storm and wind velocity. They use EM waves to detect this, but the idea is similar. Ultrasound: Waves are reflected back at different mediums, or when the type of tissue changes. This is how babies can be seen while they are developing.

Bulk of quiz: What should you know What a wave is, components of a wave, and types of waves. Wave equation, intensity of waves (richter scale and how distance affects the wave) Sound waves (hearing range, decibel scale) Timbre and Beats Interference patterns, Doppler effect, Shock waves