A wave is a periodic disturbance that moves away from a source and carries energy as it goes.
Two important categories of waves are:
Mechanical waves, which travel only through matter and involve the motion of particles of the matter they pass through. Sound waves are an example.
Electromagnetic waves, which consist of varying electric and magnetic fields and can travel through a vacuum and through matter; they do not involve the motion of particles of the matter they pass through. Light, radio waves, and X-rays are examples.
6-2. Transverse and Longitudinal Waves
Transverse waves are mechanical waves in which the particles of the matter through which they pass move perpendicular to the wave direction; transverse waves can travel only through solids.
Longitudinal waves are mechanical waves in which the particles of the matter through which they pass move parallel to the wave direction in a series of compressions and rarefactions; longitudinal waves can travel through fluids as well as solids.
Water waves are a combination of both transverse and longitudinal waves.
6-3. Describing Waves
Wavelength (l) is the distance from crest to crest (or trough to trough) of a wave.
Frequency (f ) is the number of crests that pass a given point each second; the unit of frequency (cycles per second) is the hertz (Hz).
Speed (n) is the rate at which each crest moves; wave speed is equal to wavelength times frequency:
n = lf
Period (T) is the time needed for a wave to pass a given point.
Amplitude (A) is the maximum displacement from a normal position of the particles of the medium through which a wave passes.
6-4. Standing Waves
Standing waves occur when reflected waves interact with forward-moving waves in such a way that some points in the medium have amplitudes twice that of the normal amplitude and at other points the amplitude is zero. Such waves appear to be stationary or standing still.
6-5. Sound
Sound waves are longitudinal waves.
Speed of sound is about 343 m/s (767 mi/h) in sea-level air at ordinary temperatures.
Sound travels faster in liquids and solids than in gases.
The decibel (dB) is the unit of sound intensity.
Sounds with frequencies below about 20 Hz are called infrasound; those above about 20,000 Hz are called ultrasound.
The human ear is most sensitive to sound frequencies between 3000 and 4000 Hz.
Ultrasound used in echo-sounding is called sonar.
6-6. Doppler Effect
The doppler effect is the apparent change in frequency of a wave due to the relative motion of the listener and the source of the sound.
As the relative motion reduces the distance between the source and the observer, the frequency, or pitch, of the sound becomes higher.
As the relative motion increases the distance between the source and the observer, the pitch becomes lower.
The doppler effect also occurs in light waves and is used by astronomers to calculate the speed at which stars are approaching or receding.
6-7. Musical Sounds
Musical sounds are produced by vibrating objects such as strings, vocal cords, membranes in drums, and air columns in wind instruments.
Fundamental tone is the tone produced when an object vibrates as a whole; this is always the lowest frequency.
Overtones are higher frequencies that are produced when an object vibrates in segments; they add richness and quality, or timbre, to the fundamental tone.
Resonance is the ability of an object to be set in vibration by a source whose frequency is equal to one of its natural frequencies of vibration.
The fundamental frequencies in ordinary human speech are mostly below 1000 Hz, averaging about 145 Hz in men and about 230 Hz in women.
6-8. Electromagnetic Waves
Maxwell proposed that a magnetic field is associated with a changing electric field.
Electromagnetic (em) waves consist of linked electric and magnetic fields traveling at the speed of light.
The electric and magnetic fields in an em wave form closed loops that spread out from their source with the speed of light.
The electric and magnetic fields in an em wave are perpendicular to each other and to the direction of the wave.
6-9. Types of EM Waves
In 1887, the German physicist Heinrich Hertz demonstrated the existence of em waves.
Electromagnetic waves can carry information as well as energy.
Radio communication uses amplitude modulation (AM) or frequency modulation (FM).
Amplitude modulation is the modulation of a radio wave by varying its amplitude.
Frequency modulation is the modulation of a radio wave by varying its frequency.
Radar (radio detection and ranging) is a device that uses ultra high frequency em waves to detect distant objects such as ships and airplanes.
The electromagnetic spectrum is the range of frequencies of em waves.
6-10. Light “Rays”
Light does not always travel a straight path since it can be reflected and refracted.
Light appears to travel in a straight path in a uniform medium and, although light actually consists of waves, it is useful to represent light’s straight line motion as lines called rays.
6-11. Reflection
Reflection is the change in direction of a wave when it strikes an obstacle.
The image in a mirror appears to originate from behind the mirror.
In a mirror image, left and right are interchanged because front and back have been reversed by the reflection.
6-12. Refraction
Refraction is the change in direction of a train of waves when they enter a medium in which their speed changes.
Refraction occurs when waves cross a boundary at a slanting angle; if waves approach a boundary at right angles, no refraction occurs.
Light is refracted when it goes from one medium into another medium in which the speed of light is different.
The amount of deflection when light is refracted depends on the speeds of light in the two mediums.
The index of refraction is the ratio between the speed of light in free space and its speed in a medium.
The internal reflection of light occurs when the angle through which a light ray passing from one medium to a less optically dense medium is refracted by more than 90°.
6-13. Lenses
A lens is a piece of glass or other transparent material shaped to produce an image by refracting light that comes from an object.
A converging lens is thicker in the middle than at its rim and brings parallel light rays to a single focal point, called the real focal point because the light rays pass through it, at a distance called the focal length of the lens.
A diverging lens is thinner in the middle than at its rim and spreads out parallel light rays so that they seem to come from a point behind the lens called the virtual focal point because the light rays do not pass through it but appear to do so.
6-14. The Eye
The human eye operates much like a camera and consists of the following structures:
A transparent outer membrane called the cornea.
A lens, which focuses incoming light onto the retina, which contains light-sensitive receptors.
The optic nerve, which carries nerve impulses from the retina to the brain.
Ciliary muscles, which change the shape, and thus focal length, of the lens.
The colored iris, which controls the amount of light entering the pupil or opening of the iris.
There are two common vision defects:
Farsightedness occurs when the eyeball is too short, focusing the object behind the retina and making it difficult to focus on nearby objects.
Nearsightedness occurs when the eyeball is too long, focusing the object in front of the retina and making it difficult to focus on distant objects.
Astigmatism occurs when the cornea or lens has different curvatures in different planes.
6-15. Color
White light is a mixture of light waves of different frequencies.
Each frequency of light produces the visual sensation of a particular color.
Dispersion is the separation of a beam of white light into its various colors or frequencies; rainbows are caused by the dispersion of sunlight by water droplets.
An object’s color depends on the kind of light that falls on the object and on the nature of its surface.
6-16. Interference
Interference refers to the adding together of two or more waves of the same kind that pass by the same point at the same time.
In constructive interference, the original waves are in step and combine to give a wave of greater amplitude.
In destructive interference, the original waves are out of step and combine to give a wave of smaller amplitude.
When light of only one color (one wavelength) strikes a thin film, the film appears dark where the light waves reflected from its upper and lower surfaces undergo destructive interference; the film appears bright where constructive interference takes place.
When white light strikes a thin film, the reflected waves of only one color will be in step at a particular place while waves of other colors will not; this interference results in a series of brilliant colors.
Standing waves are formed by interference.
6-17. Diffraction
Diffraction is the ability of waves to bend around the edge of an obstacle.
Diffracted waves spread out as though they originated at the corner of the obstacle and are weaker than the direct waves.
Because of diffraction, the images of microscopes and telescopes are blurred at high magnification.
The larger the diameter of a lens or mirror used in an optical instrument, the less significant the diffraction and the sharper the image.
The resolving power of a telescope depends upon the wavelength of the light that enters it divided by the diameter of the lens or mirror; the smaller the resolving power, the sharper the image.
