Vern J. Ostdiek Donald J. Bord Chapter 6 Waves and Sound (Section 1)

Vern J. OstdiekDonald J. Bord

Chapter 6Waves and Sound

(Section 1)

Sound Medicine

• The diagnosis: kidney stones, a disease that sometimes afflicts people in their 20s and 30s. • The condition is very painful, and can kill.

• Your options? • One is surgery, but the operation itself is

dangerous, and then there is a long and uncomfortable recuperation. • But since the early 1980s, there has been an

alternative that works in most cases: • You can have the stones pulverized with sound.

• No scalpels involved

Sound Medicine

• The process is called extracorporeal shock-wave lithotripsy (ESWL).

• A device called a lithotripter focuses intense sound waves on the stones, which are broken into tiny fragments that can then pass out of the patient’s system. • The sound is produced and

focused outside of the body—hence the term extracorporeal.

Sound Medicine

• Some ESWL systems make use of a reflector based on the shape of an ellipse.

• An intense sound pulse (shock wave) produced at one focus bounces off the reflector and converges on the other focus. • The reflector is positioned so that the stone is at

that second focus.

Sound Medicine

• Other lithotripters focus the sound with an “acoustic lens” in much the way a magnifying glass can be used to focus sunlight to start a fire. • In both systems, the sound is produced and

focused inside a water-filled “cushion” in similar to a balloon, that is pressed against the patient’s body.

• The sound never travels in air.

Sound Medicine

• Why does the ESWL sound wave continue on target after it passes from water into a patient? • What is it about sound waves that makes them

useful for this and many other medical applications?

• Answers to such questions are found in the study of waves.

Sound Medicine

• Waves in general and sound waves in particular are the main topics of this chapter.

• Waves are an integral part of our everyday lives. • Whether playing a guitar, listening to a radio,

clocking the speed of a thrown baseball, or having a kidney stone shattered, we are using a wave of some kind.

Sound Medicine

• The two most often used senses—sight and hearing—are highly developed wave-detection mechanisms. • In the first part of this chapter, we look at simple

waves and examine some of their general properties.

• The remainder of the chapter is about sound—how it is produced, how it travels in matter, and how it is perceived by humans.

6.1 Waves—Types and Properties

• Ripples moving over the surface of a still pond, sound from a radio speaker traveling through the air, a pulse “bouncing” back and forth on a piano string, light from the Sun illuminating and warming Earth—these are all waves.


• We can feel the effects of some waves, such as earthquake tremors (called seismic waves), as they pass. • Others, such as sound and light, we sense directly

with our ears and eyes.

• Technology has given us numerous devices that produce or detect waves that we cannot sense:• microwaves, ultrasound, x-rays


• What are waves? • Though many and diverse, they share some basic

features. • They all involve vibration or oscillation of some

kind. • Floating leaves show the vibration of the water’s

surface as ripples move by. • Our ears respond to the oscillation of air

molecules and give us the perception of sound. • Also, waves move and carry energy yet do not have

mass. • The sound from a loudspeaker can break a

wineglass even though no matter moves from the speaker to the glass.


• We can define a wave as follows: • Wave: A traveling disturbance consisting of

coordinated vibrations that transmit energy with no net movement of matter

• Sound, water ripples, and similar waves consist of vibrations of matter—air molecules or the water’s surface, for example. • The substance through which such waves travel is

called the medium of the wave. • Particles of the medium vibrate in a coordinated

fashion to form the wave.


• A rope stretched between two people is a handy medium for demonstrating a simple wave.


• A flick of the wrist sends a wave pulse down the rope. • Each short segment of the rope is pulled upward in

turn by its neighboring segment. • The forces between the parts of the medium are

responsible for “passing along” the wave.

• This kind of wave is not unlike a row of dominoes knocking each other over, except that the medium of a wave does not have to be “reset” after a wave goes by.


• Many waves—sound, water ripples, waves on a rope—require a material medium.

• They cannot exist in a vacuum. • On the other hand, light, radio waves, microwaves,

and x-rays can travel through a vacuum because they do not require a medium for their propagation.

• We will take a close look at these special waves—called electromagnetic waves—in chapter 8.


• Waves occur in a great variety of substances: • in gases (sound), liquids (water ripples), and solids

(seismic waves through rock).

• Some travel along a line (a wave on a rope), some across a surface (water ripples), and some throughout space in three dimensions (sound).• Many more examples could be listed.

• Clearly, waves are everywhere, and they are diverse in nature.


• A wave can be short and fleeting, called a wave pulse, or steady and repeating, called a continuous wave.

• The sound of a bursting balloon, a tsunami (large ocean wave generated by an earthquake), and the light from a camera flash are examples of wave pulses.

• The sound from a tuning fork and the light from the Sun are continuous waves.


• The figure shows a wave pulse and a continuous wave on a long rope. • You can see that a continuous wave is like a series

or “train” of wave pulses, one after another.


• If we take a close look at many different types of waves, we find that they can be classified according to the orientation of the wave oscillations.

• There are two main wave types: transverse and longitudinal.


Transverse Wave: A wave in which the oscillations are perpendicular (transverse) to the direction the wave travels. • Examples: waves on a rope, electromagnetic

waves, some seismic waves

Longitudinal Wave: A wave in which the oscillations are along the direction the wave travels. • Examples: sound in the air, some seismic waves


• Both types of waves can be produced on a Slinky—a short, fat spring that you may have seen “walk” down steps.

• If a Slinky is stretched out on a flat, smooth tabletop, a transverse wave is produced by moving one end from side to side, perpendicular to the Slinky’s length.


• A longitudinal wave is produced by pushing and pulling one end back and forth, first toward the other end, then back. • For each type of wave, one can produce either a

wave pulse or a continuous wave.


• A Slinky is not the only medium that can carry both transverse and longitudinal waves.

• Both kinds of waves can travel in any solid. • Earthquakes and underground explosions produce

both longitudinal and transverse seismic waves that travel through Earth.

• Simple waves that involve oscillation of atoms and molecules must be longitudinal to travel in liquids and gases because of the absence of rigid bonds between the particles.


• Many waves are neither purely longitudinal nor purely transverse. • Although a water ripple appears to be a simple

transverse wave, individual parcels of water actually move in circles or ellipses—they oscillate forward and backward as well as up and down.

• Waves in plasmas and in the atmosphere are even more complicated.

• But the two simple types of waves described here are common and well suited for illustrating wave phenomena.


• The speed of a wave is the rate of movement of the disturbance. • Do not confuse this with the speed of individual

particles as they oscillate.

• For a given type of wave, the speed is determined by the properties of the medium. • In the waves that we have been discussing, the

masses of the particles that oscillate and the forces that act between them affect the wave speed.


• As a longitudinal wave, for example, travels on a Slinky, each coil is accelerated back and forth by its neighbors. • Basic mechanics tells us that the mass of each coil

and the size of the force acting on it will determine how quickly it—and therefore the wave—moves.

• In general, weak forces or massive particles in a medium cause the wave speed to be low.


• Often, the speed of waves in a medium can be predicted by measuring some other properties of the medium. • After all, the factors that affect wave speed—

particles, masses, and interparticle forces—also affect other properties of a substance.


• For example, the speed of waves on a stretched rope or a Slinky or on a taut wire can be computed by using the force F that must be exerted to keep it stretched and its linear mass density , which equals its mass m divided by its length l. • The symbol represents the Greek letter rho,

pronounced like row.


• In particular,

• Increasing this force, also called the tension, will cause the waves to move faster. • This is how stringed instruments such as guitars

and pianos are tuned.

6.1 Waves—Types and PropertiesExample 6.1

• A student stretches a Slinky out on the floor to a length of 2 meters. The force needed to keep the Slinky stretched is measured and found to be 1.2 newtons. The Slinky’s mass is 0.3 kilograms.• What is the speed of any wave sent down the

Slinky by the student?


• First, we compute the Slinky’s linear mass density:

• The speed of waves on the Slinky is then


• The speed of sound in air or any other gas depends on the ratio of the pressure of the gas to the density of the gas. • But for each gas, this ratio depends only on the

temperature.

• In particular, the speed of sound in a gas is proportional to the square root of the Kelvin temperature:

in m/s, in kelvins

v T

v T


• For air,

• Although the air is thinner at higher altitudes, the speed of sound there is actually lower because the air is colder at these elevations.


• What is the speed of sound in air at room temperature (20C = 68F)? • The temperature in kelvins is

• Therefore,


• The numerical factor (20.1) in the equation in Example 6.2 is determined by the properties of the molecules that comprise air and therefore applies to air only.

• The speed of sound in any other gas will be different, and the corresponding equation for v will have a different numerical factor. • Two examples:


• For the remainder of this section, we will take a look at some of the properties of a continuous wave.

• A convenient example is a transverse wave on a Slinky produced by moving one end smoothly side to side.


• The figure shows a “snapshot” of such a wave. • It shows the shape of the Slinky at some instant in

time. • Note that the wave has the same sinusoidal shape

you’ve seen before.


• The high points of the wave are called peaks or crests, and the low points are called valleys or troughs.

• The straight line through the middle represents the equilibrium configuration of the medium—its shape when there is no wave.


• In addition to wave speed, there are three other important parameters of a continuous wave that can be measured: • amplitude, wavelength, and frequency

• At any moment, the different particles of the medium are generally displaced from their equilibrium positions by different amounts.

• The maximum displacement is called the amplitude of the wave. Amplitude: The maximum displacement of points on a wave measured from the equilibrium position.


• The amplitude is just a distance equal to the height of a peak or the depth of a valley, which are the same for a pure wave.

• The amplitude of a particular type of wave can vary greatly. • For water waves, it can be a few millimeters for

ripples to tens of meters for ocean waves.

• When we hear a sound, its loudness depends on the amplitude of the sound wave: • Louder sounds have larger amplitudes.


Wavelength: The distance between two successive “like” points on a wave. • For example, the distance between two adjacent

peaks or two adjacent valleys. • Wavelength is represented by the lowercase Greek

letter lambda ().


• There is also a large variation in the wavelengths of particular types of waves. • The wavelengths of sound (in air) that can be heard

by humans range from about 2 centimeters (very high pitch) to about 17 meters (very low pitch).

• Typical wavelengths for radio waves are 3 meters for FM stations and 300 meters for AM stations.


• Any segment of a wave that is one wavelength long is called one cycle of the wave.

• As each cycle of a wave passes by a given point in the medium, that point makes one complete oscillation—up, down, and back to the starting position. • The figure shows three complete cycles of a wave.


• Amplitude and wavelength are independent features of a wave: • A short-wavelength wave

can have a small or a large amplitude.


• To understand what the frequency of a wave is, we must “unfreeze” the wave and imagine it as it moves along.

• The rate at which the wave cycles pass a point is the frequency of the wave. • Recall that the unit of measure of frequency is the

hertz (Hz).

Frequency: The number of cycles of a wave passing a point per unit time.• The number of oscillations per second in the wave.


• If you move the end of a Slinky back and forth three times each second, you will produce a wave with a frequency of 3 hertz. • The note A above middle C on a modern piano has

a frequency of 440 hertz. • This means that 440 cycles of the sound wave

reach your ear each second.

• The piano wires producing the sound and the air molecules in the room all vibrate with the same frequency: 440 hertz.


• Under ideal conditions, a person with good hearing can hear sounds with frequencies as low as 20 hertz or as high as 20,000 hertz.

• Frequency is important in other kinds of waves as well. • Each radio station broadcasts a radio wave with a

specific frequency—for example:• 1,100 kilohertz = 1,100,000 hertz, or • 92.5 megahertz = 92,500,000 hertz.


• Amplitude, wavelength, and frequency can be identified for both transverse waves and longitudinal waves, although the amplitude of a longitudinal wave is a bit difficult to visualize. • It is still the maximum displacement from the

equilibrium position, but in this case the displacement is along the direction the wave is traveling.


• The figure shows a closeup of a Slinky with no wave and then with a longitudinal wave traveling on it. • The amplitude is the farthest distance that any coil

is displaced to the right or left of its equilibrium position.


• The regions where the coils are squeezed together are called compressions, and the regions where they are spread apart are called expansions or rarefactions. • The wavelength is the distance between two

adjacent compressions or two adjacent expansions.


• The speed of a wave, its wavelength, and its frequency are related to each other in a simple way. • Imagine a continuous wave passing by a point,

perhaps ripples moving by a plant stem. • The speed of the wave equals the number of cycles

that pass by each second multiplied by the length of each cycle.


• For example, if five cycles pass the stem each second and the peaks of the ripples are 0.03 meters apart, the wave speed is 0.15 m/s.


• In general, wave speed = number of cycles per second × length of each cycle• The two quantities on the right of the equal sign are

the frequency of the wave and the wavelength, respectively.

• Therefore,

• The velocity of a continuous wave is equal to the frequency of the wave times the wavelength.


• In many cases, all waves that travel in a particular medium have the same speed. • Wave pulses, low-frequency continuous waves, and

high-frequency continuous waves all travel with the same speed.

• Sound is an important example of this; sound pulses, low-frequency sounds, and high-frequency sounds travel through the air with the same speed, • 344 m/s at room temperature


• Similarly, light, radio waves, and microwaves travel with the same speed in a vacuum:

3×108 m/s. • According to the equation v = f, when the wave

speed is the same for all waves, higher frequency waves must have proportionally shorter wavelengths. • A 20-hertz sound wave has a wavelength of about

17 meters, whereas a 20,000-hertz sound wave has a wavelength of about 1.7 centimeters.

6.1 Waves—Types and PropertiesExample 6.3• Before a concert, musicians in an orchestra tune

their instruments to the note A, which has a frequency of 440 hertz. • What is the wavelength of this sound in air at room

temperature? • The speed of sound at this temperature is 344

m/s, so:

• The wavelength of sound with a frequency of 220 hertz is twice as large: 1.56 meters.


• Not all continuous waves have the simple sinusoidal shape shown in the figure below. • In fact, waves with precisely that shape are

relatively rare.

• Any continuous wave that does not have a sinusoidal shape is called a complex wave.


• The figure shows two examples. • Note that there are three different-sized peaks in

each cycle of the upper wave.

• The shape of a wave is called its waveform. • The two complex waves in the figure have about

the same wavelength and amplitude, but they have very different waveforms.


• The waveform is another feature that is needed when comparing complex waves.

Concept Map 6.1

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Vern J. Ostdiek Donald J. Bord Chapter 6 Waves and Sound (Section 1)