Question #1. Watch the video titled “Video Tour of the Electromagnetic Spectrum” (5 min 03 s). Be prepared to discuss.

PHS101_Week4__Waves_Slides.ppt

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Introduction to Physical Science

PHS 101

Wave Motion, and Sound

Welcome to Introduction to Physical Sciences. In this week’s lesson we will discuss heat, temperature, wave motion, and sound.

Objectives

Upon completion of this lesson you will be able to:
Describe the physical basis for phenomena that are unique to waves, including interference and the Doppler effect

Upon completion of this lesson you will be able to:

Give examples of how the physical laws governing motion, energy and heat relate to everyday happenings

Describe the physical basis for phenomena that are unique to waves, including interference and the Doppler effect

Please go to the next slide.

Forces and Vibrations

Vibration - repetitive back and forth motion
At the equilibrium position, spring is not compressed
When disturbed from equilibrium position, restoring force acts toward equilibrium
Carried by inertia past equilibrium to other extreme
Example of “simple harmonic motion”

Again, you undoubtedly have an intuitive understanding of what the term vibration means. When something vibrates, it has a characteristic back and forth motion that repeats over and over again. In fact, this motion can be in any direction, and if external forces such as friction were removed, it could continue on indefinitely.

Let’s look more closely at vibration. Let’s consider, for example, the string of a harp or guitar. When not being played, the string is at its equilibrium position. When you pluck or pick the string, you apply a force that deforms it or moves it away from equilibrium. When you let go, the restoring force pulls it back to equilibrium where force is now zero but the string has a maximum velocity and inertia that carries it past resting and beyond. The string is now stretched in the opposite direction and the restoring force will begin to act once again. In the real world, you note that the path the string follows will get shorter and shorter due to frictional forces. But if you took those out of the picture, or added additional force, the string would vibrate indefinitely with a repeating or periodic motion.

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Describing Vibrations

Variables describing vibration include:
Amplitude
Cycle
Period
Frequency in hertz (Hz)
Period and frequency both describe time factors and are inversely proportional

Several variables are measured to allow quantitative description of the motion of a vibrating mass. These variables are:

Amplitude- this is the maximum extent of displacement, or movement, away from the equilibrium position. The greater the displacement, the greater the amplitude.
Cycle- one complete vibration. It begins with displacement of the mass to one side, let’s say the left, then through the complete swing over to the right, and then back to the starting point.
Period- this is the time it takes to complete one cycle.
Frequency- the number of cycles per second which is measured in units called hertz.

Period and frequency are both variables that describe time factors. They are related through the mathematical statement time equals one divided by frequency. Expressed as an equation, T equals one over f.

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Waves

Wave- a disturbance that moves through a medium
Can be caused by:
Periodic motion like a vibration
Pulse- single event of short duration
Waves are traveling disturbances
Waves transport energy without transporting matter

There are two main ways that energy can be transported from one point to another. The first is through the movement of particles of matter. The second way is through waves. A wave is a disturbance that moves through a medium. That medium can be a solid, a liquid, or a gas. While the wave moves, the matter composing the medium does not.

The best way to understand this concept is to think of a common example. And this is one you can illustrate for yourself in your sink or bath tub. First, fill your tub (or sink) with water. Let it sit so that the surface is as undisturbed as possible. Now, float a light object like a leaf or piece of paper gently on the surface. Next, drop a penny in. As the penny strikes the water, you see a circular wave traveling outward followed by other, concentric waves. As this happens, watch the floating leaf or paper. It bobs up and down on the surface, but note that it stays in one place and does not move outward. This shows you that the water molecules, the actual matter composing water, is staying stationary. It is not traveling outward with the movement of the waves.

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Kinds of Waves

Longitudinal wave- molecules of medium move back and forth in the same direction as the wave
Transverse wave- motion of medium is perpendicular to direction of the wave

There are two kinds of waves that differ in the pattern of motion of the medium with respect to the direction of the wave motion.

In longitudinal waves, the molecules of the medium move back and forth, closer together and then farther apart, in the same direction and plane of motion as the wave. Think again of a Slinky. This time it is stretched out on the floor with a friend holding the other end. If you sharply push your end of the Slinky and then draw back, a wave of compressed coils travels along the length toward your friend. Note that each individual coil stays in place, it is just the wave motion that travels.

In transverse wave motion, the molecules of the medium move in a direction perpendicular to the wave motion. The surface water waves produced by tossing a penny in your bath tub are examples.

Gases and liquids support longitudinal wave motion. Solids can support either.

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Waves in Air

Longitudinal waves move through air, including sound waves
Molecules of air vibrate back and forth parallel to direction of wave motion
Move closer together and then farther apart
Condensation- regions of crowded molecules
Rarefaction- regions of widely spaced molecules

Air is a gaseous medium, and as we just discussed gas supports longitudinal wave motion. Sound waves travel through air as longitudinal waves.

A sound wave, or pressure wave traveling through air creates pulses of molecular movement in which molecules alternately move close together and then farther apart. To illustrate this, let’s think of a tuning fork. When you strike a tuning fork on a hard surface, its tines vibrate. As a tine vibrates outward, it exerts pressure on nearby air molecules and crowds them together. A wave of “crowding”, called condensation, quickly travels outward through the air. As the tine vibrates in the opposite direction, it causes the air molecules next to it to spread out. A wave of “spreading out”, called rarefaction, travels outward through the air. So the tuning for sends out repeated pulses of condensation and rarefaction that travel through the surrounding air. You know that these pulses are transmitting energy. How do you know? They make your ear drums vibrate (mechanical energy) with the result that you can hear the sound!

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Hearing Waves in Air

Range of human hearing- 20 to 20,000 Hz
Sound is a pressure wave that falls within this range
Sound waves converted to mechanical vibrations by tympanic membrane (ear drum)
Vibrations cause action potentials in organ of corti in inner ear
Temporal lobe of brain- integrates signals as sound

Sound waves are pressure waves traveling through air. The human ear can hear sounds with frequencies between twenty and twenty thousand hertz. When sound waves enter the auditory canal, they cause the tympanic membrane to vibrate. Each pitch of sound creates a specific intensity of vibration. The tympanic membrane, therefore, converts the sound waves to mechanical vibrations which are transmitted across the middle ear by the actions of three small bones, the malleus, the incus, and the stapes. These form a bridge across the middle ear and attach to the oval window, the entrance to the inner ear. The inner ear is fluid filled, and it is within the cochlea of the inner ear that the receptors for the sense of hearing lie. These are called the organ of corti, and are composed of fibers of increasing length. Each fiber vibrates in response to sound of a specific pitch. Vibrations of the oval window are transmitted to the fluid of the cochlea, and this results in vibration of specific fibers of the organ of corti. Each fiber, in turn, is connected to an auditory neuron that carries information to the temporal lobe of the brain. The auditory cortex of the brain then interprets the signals as sound.

Other species can hear pressure waves outside our range of hearing. You probably already know your dog can hear sounds of much higher pitch than you can. Of particular note are species of bats and whales that have a form of “sonar” or “radar” that allows them to hear sounds well above the range of human hearing.

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Describing Waves

Variables used to describe waves
Wavelength- length in which wave repeats itself, distance from peak to peak
Amplitude- displacement from rest to crest or rest to trough
Frequency- number of cycles per second
Period- time for wave to repeat itself
Wave equation

Variables that are used to quantify and describe waves include:

Wavelength – this is the distance measured from one wave peak to the next peak, or the length in which the wave repeats itself. It is measured in distance units, usually centimeters or meters. Wavelength is represented by the symbol lambda.
Amplitude- this is the displacement measured from rest to crest, or from rest to trough.
Frequency- the number of cycles per second, measured in hertz.
Period- this is the time for the wave to repeat itself.

The relationship between wavelength, period, and speed is expressed mathematically as velocity is equal to wavelength times frequency. This is called the wave equation.

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Sound Waves

Sound waves require medium for transmission
Nature of medium determines transmission
Inertia of molecules
Strength of molecular interaction
Velocity of sound in air

Sound waves require a medium for transmission from one point to another. This medium can be a solid, liquid, or gas but not all media have equal capabilities for transmitting sound waves. Two main variables determine if a medium will conduct sound efficiently. These are the inertia of the molecules of the medium and their intermolecular attraction.

Large molecules have more inertia than small molecules, and so substances composed of larger molecules may conduct sound more slowly. Gases, with widely spaced molecules with low levels of interaction may also conduct sound slowly in comparison with media with more intermolecular contact. Solids, as a rule, conduct sound rapidly because their molecules are closely bound together and wave motion travels quickly from molecule to molecule.

Dry air at zero degrees Celsius will conduct sound at the rate of one thousand and eighty seven feet per second. The temperature of air affects the rate of sound conduction because it affects the kinetic energy of the air molecules. The molecules of warm air have greater kinetic energy and therefore more molecular motion, and so warm air conducts sound more rapidly than cool air. For each degree Celsius increase in temperature, sound travels 2 feet per second faster.

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Refraction and Reflection

Sound wave- spherical waves moving out from source
Wave front- crest of each condensation
Wave motion traced with wave fronts
Far from source, wave front becomes planar
Boundary- division between two physical conditions
Between different materials
Between same material but different conditions
When wave strikes boundary, it can be:
Refracted
Reflected
Absorbed

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Please insert fig. 5.11 on pg 112

The waves that were generated by dropping a penny into your bath tub were two-dimensional. They radiated out from the source in a concentric circular pattern. Sound waves emanate from a source, too, but they are three-dimensional waves and so are described as spherical. By identifying a specific part of a sound wave, like the crest of each condensation, you have identified a wave front. From one crest to the next is one wavelength. As each wave front travels farther from the source, they begin to become more linear, or planar, and less rounded.

As they travel, waves may encounter boundaries that will affect how they proceed. A boundary is a division between two different physical conditions. This may be a point where one medium adjoins a different medium as in an air-water interface, or it could be different conditions within a single medium as in a region of temperature change. When a wave front strikes a boundary, three things can happen:

the wave front may undergo refraction, which is a bending that changes the direction of travel.
The wave front may undergo reflection if the wave front is parallel to the boundary and bounce backward. If the reflected sound mixes with additional incoming waves it produces reverberation. If it does not mix, it causes an echo.
The wave front may be absorbed and not travel farther.

Any combination of the three may also occur.

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Interference

Constructive interference
Peaks and troughs of one aligned with those of another
Enhances
Destructive interference
Peaks of one aligned with troughs of another
Cancels out and diminishes
Beats
Regularly spaced increase and decrease in sound
Beat frequency is the difference between frequencies of two interfering waves

When two or more waves interact, wave interference occurs. Interference in common usage evokes a negative image, but in wave function this is not always the case.

When two waves interact and their peaks and troughs are aligned, peak to peak and trough to trough, this is called constructive interference. The total wave function is enhanced, and the waves are said to be in phase with eachother.

When two waves interact and the peaks of one are aligned with the troughs of the other, this is destructive interference and the waves are described as being out of phase.

Two waves that are alike in all ways except frequency can produce regularly spaced increases and decreases in sound. These are called beats. The frequency of the beat is the difference between the frequencies of the individual waves.

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Energy and Sound

Intensity- energy of sound wave
Measured in watts per square meter and proportional to square of amplitude
Loudness is subjective perception related to
The energy of vibrating object
Conditions of the air
How far away source is
Intensity measure by decibel scale
Logarithmic scale means simpler numbers

Intensity is a measurement of the amount of energy that is transported through a medium at a given point per unit time. The greater the amplitude of vibrations the faster the rate at which energy is transmitted and the more intense the sound. Intensity is the energy per unit time per area. Since energy per unit time is the definition of power, we can say intensity is the power per area. This is expressed in units of Watts per meter squared.

Loudness of sound is related to the energy of the vibrating object as we have just seen, and we previously discussed how conditions of the air like temperature can affect transmission and therefore loudness of sound. Distance is also a factor in perception of loudness of sound. Intensity decreases the farther away you are from the source.

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Resonance

All objects vibrate with characteristic frequency or set of frequencies
Called natural frequency
Depends on substance and shape
When frequency of applied force matches the natural frequency of the object, energy transfer is efficient
Called resonance

When a bow is drawn over a violin string, when a guitar string is plucked, and when a tuning fork is struck, these objects will begin to freely vibrate at a constant frequency. This frequency is called the natural frequency. All material objects will vibrate at a characteristic natural frequency or group of frequencies when sufficient force is applied in some way.

The natural frequency of vibration of an object depends upon the substance it is composed of and its shape. The composition of the substance determines the speed at which energy is conducted and the shape or length affects the wavelength. For example, a loud explosion may cause one window to shatter but not another. Why does one break and the other not? The differ in their natural frequency of vibration.

When the frequency of the applied force matches the natural frequency of an object, energy is transferred very efficiently. This situation is called resonance.

So can you really hear the ocean inside a sea shell? A romantic notion, yes, but unfortunately what you hear is just an example of resonance. Some noise in your environment has a natural frequency which causes the molecules of the shell to become disturbed and vibrate, and that’s what you hear. But it’s more fun to pretend you are hearing the sea!

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Sources of Sound

Sound produced by vibrating objects
If frequencies fall in range of human hearing, produces sound
Random, irregular vibrations of multiple frequencies- unpleasant noise
Resonance of single or small set of frequencies- musical
Sounds- combinations of pure frequencies

Interestingly, we tend to think of objects that vibrate at a single resonant frequency, or perhaps just a few resonant frequencies, as musical and thus pleasing to the ear. A flute is an example of an instrument that vibrates at single resonant frequencies and so has a very pure tone. A tube vibrates at a set of resonant frequencies and much less clarity of tone but is still pleasant to listen to. When a stack of dishes crashes to the floor, they vibrate at many resonant frequencies and the result is not exactly m.usic to the ear.

The pitch of sound can change with shape or length of the object. Here’s something you can try at home. Line up a few plastic water or soda bottles and fill then with different amounts of water. Blow across the top of each bottle. When you blow, this disrupts air molecules in the column of air inside the bottle. Vibrations are produced and you hear these as sound. Note the differences between the tones produced between bottles. The longer the column of air (and the less water), the lower the tone and vice versa.

This relationship between length and pitch holds true for strings on a harp. The shorter the string, the shorter the wavelength and the higher the pitch.

Vibrating Strings

Vibrations in strings with fixed ends
Multiple waves present simultaneously
Waves reflected backward at ends
Reflected waves and incoming waves interact
Standing waves
Produced at resonant frequencies
Commonly called harmonics
Points of destructive interference- nodes
Points of constructive interference- anti-nodes

We will now consider what happens in vibrations are generated in strings that have fixed ends. As a wave travels along the string, it will be reflected when it hits the fixed end. The reflected wave then travels backward along the string. If this reflected wave meets a second incoming wave of the same amplitude and frequency, a standing wave will result.

A standing wave is so named because at points along the wave pattern are nodes that appear to be standing still. These nodes are the result of destructive interference between the reflected wave and an incoming wave. Between the nodes are areas of constructive interference called anti-nodes. The anti-nodal regions rapidly alternate up and down, but do not travel along the string.

One standing wave consists of three nodes and two anti-nodes. They are produced at the resonant frequencies of the string which are determined by the material the string is composed of, the length of the string, and the tension on the string.

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Resonance of Vibrating Strings

Fundamental frequency- lowest frequency produced by an object
Consists of two nodes and one anti-node
Has the longest wavelength and lowest frequency

The fundamental frequency is the lowest possible frequency and therefore the longest wavelength than an object can produce. Let’s imagine, again, a guitar string. The longest wavelength and lowest frequency vibration of that string would consist of two nodes, one at each end, and a single long anti-node between them.

When discussing musical instruments, the fundamental frequency is called the first harmonic. The pattern produced at this fundamental frequency, then, really looks like half of a standard wave pattern. Remember, a standard wave pattern starts at a node, rises to a crest, falls back to a node, then goes down to a trough and then back up to a node: three nodes and two anti-nodes. The fundamental frequency begins at a node, rises to a crest, and then back to a node.

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Sounds From Moving Sources

The Doppler Effect
Changing wave pattern from moving source
As object approaches, sound has higher frequency
As object travels past, frequency decreases
Supersonic speeds
Sound waves condense and form burst

You have undoubtedly noticed how when you hear a train whistle, a fire engine’s siren, or a jet taking off that the pitch of sound seems to change as the object goes by. It seems to go from a higher pitched sound to a lower pitched one as it travels past. This is due to the Doppler effect, named after the physicist Christian Johann Doppler who first described it.

The Doppler effect occurs when sound is emanating from a moving source. Remember that sound waves are spherical, and each burst of sound travels outward as a series of crests. When you are standing in front of the source, the crests are clustered, or bunched together so the sound will be higher pitched than if the source was standing still. As it moves by, the crests emitted at a new point will be more stretched out, and have a lower pitch. This continues as the object moves on past and away.

Now, suppose the source of sound is a super sonic jet airplane. Super sonic means moving faster than the speed of sound. If the source of sound is moving faster than sound itself, the sound waves literally pile up and produce one huge shock wave. This is called a sonic boom. Years ago, military exercises produced sonic booms across the land, but they were so disruptive that supersonic speeds are now prohibited over inhabited areas of the country.

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Summary

Kinetic molecular theory, molecules and molecular interactions and movement, phases of matter
Temperature and thermometers
Heat, measures of heat, specific heat, heat flow
Energy, heat, and molecular theory
Phase change- evaporation, condensation, relative humidity
Thermodynamics
Force and elastic materials
Forces and vibrations- describing vibrations
Waves- kinds of waves, waves in air, hearing waves in air, describing waves, refraction and reflection, and interference
Energy and sound- resonance, sources of sound, vibrating strings
Sounds from moving sources

We have now reached the end of this lesson. Let’s take a look at what we have covered.

We began our discussion by examining the kinetic molecular theory and studying molecular interactions, molecular movement, and the three different phases of matter; solid, liquid, and gas.

We then turned our attention to a discussion of temperature and how it is measured. We defined three different temperature scales; Fahrenheit, Celsius, and Kelvin and determined how to interconvert temperatures from one scale to another.

Next, we discussed heat, measures of heat, and defined specific heat of matter. We looked at heat flow, and described three mechanisms; conduction, convection, and radiation.

We then looked at the relationships between energy, heat, and the molecular theory. We considered internal and external energy and the ability to do work.

From there, we looked at phase changes and how they occur. We defined evaporation, condensation, and relative humidity.

Next we discussed thermodynamics and looked at applications of the first and second laws of thermodynamics.

After that, we examined force and elastic materials, and how these materials are able to regain original shape after being deformed. We related this to force and vibrations and described characteristics that describe vibrations.

We discussed waves, how they form, and their characteristics. We looked at waves in air and how we hear those within the frequency range of human hearing. We examine different sources of sound and used vibrating strings as our example.

Lastly we examined the Doppler effect and how sound from a moving source appears to change frequency.