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What we do in life will echo in eternity -- as quoted by Maximus Decimus Meridius in the film Gladiator. Activity Create a causal chain of events (cause and effect) at least 5 events long. Each successive event must be a reasonable consequence of the preceding event. Energy Transfer.
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What we do in life will echo in eternity-- as quoted by Maximus Decimus Meridius in the film Gladiator Activity Create a causal chain of events (cause and effect) at least 5 events long. Each successive event must be a reasonable consequence of the preceding event.
Energy Transfer There are two manners in which energy can be transferred from one point in space to another: • A mass, a tennis ball for example, is given energy and that mass travels through space and transfers that energy to another point. • Energy itself travels through space – at times with the assistance of an oscillating medium (for example, a bunch of high school students lined up shoulder to shoulder) and at times energy travels through nothingness, with seemingly no help at all (like light from the sun). In both these examples, energy is being transferred from one point to another in the form of a wave.
Wave Motion wave motion is a means of transferring energy There are two types of waves – Mechanical Waves and Electromagnetic waves. • Mechanical waves require a medium through which to propagate • mechanical waves cannot travel through a vacuum – that’s why in space, no one can hear you scream. • In mechanical waves, the energy to be transferred originates as a vibration or oscillation which sets up a disturbance in the medium. • The disturbance travels through the medium as a wave. • The medium itself, however, does not move forward with the wave, but vibrates about equilibrium positions.
Electromagnetic waves do not require a medium through which to propagate • Electromagnetic waves can travel through a medium – that’s why light can move through water and air, or x-rays can penetrate the body – but these waves travel their fastest in a vacuum, and slow down upon encountering any type of medium • Electromagnetic waves are somewhat more complex than mechanical waves, after all, light somehow manages to travel the empty vacuum of space starting at the sun and making it’s way all the way to the earth. We’ll delve more deeply into e&m waves later on. • All energy transfer occurring in the form of wave motion, whether mechanical or electromagnetic, have similar characteristics and all forms of wave motion abide by the same laws and principles. This allows us to learn all there is to know about waves by analyzing waves on a spring.
“Cause is the effect concealed, effect is the cause revealed” The source of all wave motion is a vibrating or oscillating phenomenon. In the case of waves on a spring the oscillating phenomenon is your hand or wrist; in the case of light or any other electromagnetic wave, the oscillating phenomenon is an electron (to be discussed in more detail); in the case of ripples created in a pond while you sit on a raft and laze the day away, the oscillating phenomenon is your finger dipping in and out of the water; in the case of sound produced from your mouth, the oscillating or vibrating source is your larynx. Since the source of wave motion is periodic and cyclic, it stands to reason that the wave itself is also periodic and cyclic. The preceding point is of great importance – a fundamental characteristic of wave motion is that waves repeat themselves over and over and over again. The following characteristics help us better understand the cyclic and periodic behavior of wave motion.
Wave Characteristics Amplitude – the maximum displacement from the rest or equilibrium position. The larger the amplitude the more energy carried by the wave and the more energy it took to create the wave. • The amplitude of a light wave is associated with the brightness (or intensity) of the light • The amplitude of a sound wave is associated with how loud the sound is
wavelength -- the shortest distance between points where the wave pattern repeats itself. or, the distance between two successive points that are in the same phase of vibration. or, the distance traveled within which one wave cycle has been completed.
Frequency (f) – the number of complete cycles per second. -- the cycles per unit of time Frequency is measured in hertz. One hertz (Hz) is one vibration per second. The frequency of a wave, will be the same as the frequency of the oscillating source. The frequency of a light wave is associated with color The frequency of a sound wave is associated with pitch
Period (T) – the time per cycle (time per vibration; time per oscillation) The period is measured in seconds (s). The frequency (cycles per time) and period (time per cycle) are reciprocals of each other. T = 1/f
Crests – high points of each wave motion Troughs – low points of each wave motion Each crest is one wavelength from the next crest (same with troughs).
The frequency of a wave is determined by the oscillating or vibrating source – this means that the wave has the same frequency as the vibrating phenomenon that created it. As an example: If you strike middle c on a piano, the string that the hammer strikes is designed to vibrate 256 time per second. The sound wave that is created as a result has a frequency of 256 Hz. Wave speed is determined by the medium through which the wave travels. Let’s derive the equation for wave speed.
Practice Problemsfrequency, wavelength, wave speed • The needle of a sowing machine moves up and down periodically. Its driving force comes from a rotating wheel that is powered by an electric motor. How do you suppose the period of the up and down needle compares to the period of the rotating wheel? • If a gas tap is turned on for a few seconds, someone a couple of meters away will hear the gas escaping long before she smells it. What does this indicate about the speed of sound and the motion of the molecules in the sound-carrying medium? • If we double the frequency of a vibrating object, what happens to its period? • Red light has a longer wavelength than violet light. Which has a greater frequency? • You dip your finger repeatedly in a puddle of water and make waves. What happens to the wavelength if you dip your finger more frequently? • How does the frequency of vibration of a small object floating in water compare to the number of waves passing it each second?
How far in terms of wavelength does a wave travel in one period? • Why is lightning seen before thunder is heard? • What is the frequency in hertz that corresponds to the following periods: .1s, 5s, 1/60 s? • A skipper on a boat notices wave crests passing his anchor chain every 5 seconds. He estimates the distance between wave crests to be 15 m. He also correctly estimates the speed of the waves. What is the speed? • On a keyboard, you strike middle C, whose frequency is 256 Hz. • What is the period of one vibration of this tone? • As the sound of leaves the instrument at a speed of 340 m/s, what is its wavelength in air? • If you were foolish enough to play your keyboard instrument under water, where the speed of sound is 1,500 m/s, what would be the wavelength of the middle C tone in water? Explain why middle C (or any other tone) has a longer wavelength in water than in air.
Additional Problems – wave speed, frequency, period and wavelength • A cat can hear sound frequencies up to 70,000 Hz. Bats send and receive ultrahigh-frequency squeaks up to 120,000 Hz. Which hears sound of shorter wavelengths, cats or bats? • Sound from source A has twice the frequency of sound from source B. Compare the wavelengths of sound from the two sources. • Suppose a sound wave and an electromagnetic wave have the same frequency. Which has the longer wavelength? • If a bell is ringing inside a bell jar, we can no longer hear it when the air is pumped out, but we can still see it. What differences in the properties of sound and light does this indicate? • What two physics mistakes occur in in a science fiction movie that shows a distant explosion in outer space, where you see and hear the explosion at the same time?
What is the wavelength of a 340 Hz tone in air? What is the wavelength of a 340,000 Hz ultrasonic wave in air? • An oceanic depth-sounding vessel survey the ocean bottom with ultrasonic waves that travel 1,530 m/s in seawater. How deep is the water directly below the vessel if the time delay of the echo to the ocean floor and back is 6 s? • The highest frequencies humans can hear is about 20,000 Hz. What is the wavelength of sound in air at this frequency? What is the wavelength for the lowest sounds we can hear, about 20 Hz?
SPEED OF SOUND The Speed of Sound A sound wave is a pressure disturbance which travels through a medium by means of particle interaction. As one particle becomes disturbed, it exerts a force on the next adjacent particle, thus disturbing that particle from rest and transporting the energy through the medium. Like any wave, the speed of a sound wave refers to how fast the disturbance is passed from particle to particle. While frequency refers to the number of vibrations which an individual particle makes per unit of time, speed refers to the distance which the disturbance travels per unit of time. Always be cautious to distinguish between the two often confused quantities of speed (how fast...) and frequency (how often...). Since the speed of a wave is defined as the distance which a point on a wave (such as a compression or a rarefaction) travels per unit of time, it is often expressed in units of
meters/second (abbreviated m/s). In equation form, this is speed = distance/time The faster a sound wave travels, the more distance it will cover in the same period of time. If a sound wave is observed to travel a distance of 700 meters in 2 seconds, then the speed of the wave would be 350 m/s. A slower wave would cover less distance - perhaps 600 meters - in the same time period of 2 seconds and thus have a speed of 300 m/s. Faster waves cover more distance in the same period of time. The speed of any wave depends upon the properties of the medium through which the wave is traveling. Typically there are two essential types of properties which effect wave speed - inertial properties and elastic properties. The density of a medium is an example of an inertial property. The greater the inertia (i.e., mass density) of individual particles of the medium, the less responsive they will be to the interactions between neighboring particles and the slower the wave. If all other factors are equal (and seldom is it that simple), a sound wave will travel
faster in a less dense material than a more dense material. Thus, a sound wave will travel nearly three times faster in Helium as it will in air; this is mostly due to the lower mass of Helium particles as compared to air particles. Elastic properties are those properties related to the tendency of a material to either maintain its shape and not deform whenever a force or stress is applied to it. A material such as steel will experience a very small deformation of shape (and dimension) when a stress is applied to it. Steel is a rigid material with a high elasticity. On the other hand, a material such as a rubber band is highly flexible; when a force is applied to stretch the rubber band, it deforms or changes its shape readily. A small stress on the rubber band causes a large deformation. Steel is considered to be a stiff or rigid material, whereas a rubber band is considered a flexible material. At the particle level, a stiff or rigid material is characterized by atoms and/or molecules with strong attractions for each other. When a force is applied in an attempt to stretch or deform the material, its strong particle
interactions prevent this deformation and help the material maintain its shape. Rigid materials such as steel are considered to have a high elasticity (elastic modulus is the technical term). The phase of matter has a tremendous impact upon the elastic properties of the medium. In general, solids have the strongest interactions between particles, followed by liquids and then gases. For this reason, longitudinal sound waves travel faster in solids than they do in liquids than they do in gases. Even though the inertial factor may favor gases, the elastic factor has a greater influence on the speed (v) of a wave, thus yielding this general pattern: vsolids > vliquids > vgases The speed of a sound wave in air depends upon the properties of the air, namely the temperature and the pressure. The pressure of air (like any gas) will effect the mass density of the air (an inertial property) and the temperature will effect the strength of the particle interactions (an elastic property). At normal atmospheric pressure, the temperature dependence of the
speed of a sound wave through air is approximated by the following equation: v = 331 m/s + (0.6 m/s/C)*T where T is the temperature of the air in degrees Celsius. Questions to Guide Your Reading: 1. With reference to the sound wave, discuss the difference between the speed of the sound wave and the frequency of the wave -- focus on the definition given in the reading. 2. What properties of the medium is the speed of a wave dependent upon? How do these properties affect the speed of the wave? Be sure you refer to the interaction of the particles of the medium and the mass density of the medium (and how they affect the speed of a wave) when answering this question. 3.Explain why the speed of sound is greatest in solids, then liquids and slowest in gases. 4. Does sound travel faster in winter or in summer? Make sure you explain the mechanics of how temperature affects the speed of sound in your answer.
