Resources: The Physics Classroom, Daniel A. Russell
How much more energy per unit time does the wave on the left transmit? Since its amplitude is twice as large, it transmits 4 times the energy
The upper wave has 2 x the frequency of the bottom. Note that the x-axis has units of time in this graph.
Examples: Speed of wave in string depends on tension and linear density. Speed of wave in fluid depends on bulk modulus and density. Speed of wave in solid depends on elastic modulus and density.
Recall that speed v = distance traveled/time, or v = wavelength/period = wavelength x frequency
Answer: 2 complete wavelengths are shown
What is a Wave?• Wave: motion of a disturbance– Disturbance creates waves thattravel away from the source of thedisturbance• Waves transport energy, not matter.• Mechanical waves require amedium: the elastic, deformablematter through which disturbancetravels• Electromagnetic waves don’trequire a medium
Longitudinal Wave• Medium moves parallel todirection wave travels• Examples: sound, p-waves• Have compressions andrarefactions
Longitudinal Waves (cont.)• Additional terms with longitudinal waves:• Compression: where wave fronts arecloser together than in undisturbedmedium• Rarefaction: where they are farther apartthan in undisturbed medium
Representing a Longitudinal Waveas a Sine Wave
Wave ParametersThe following parameters are used todescribe waves:–Amplitude–Wave length–Frequency–Period–Speed
Amplitude (A)• How “tall” (or “wide”) the wave is• Maximum displacement from the averageor equilibrium position–Crests: highs–Troughs: lows–Measured from “crest to rest” or “troughto rest”• Unit of measure: meter
Amplitude (cont.)• These waves differ only in their amplitude:the “taller” wave has the greater amplitude• The amount of energy a wave transmits isrelated to its amplitude (proportional to A2)-3.0-2.0-1.00.01.02.03.00.0 5.0 10.0 15.0 20.0-3.0-2.0-1.00.01.02.03.00.0 5.0 10.0 15.0 20.0Amplitude = 2.0 cm Amplitude = 1.0 cmHow much more energy does the wave on theleft transmit? 4 times as much
Wave Length (λ)• Distance wave travels inone cycle• Distance from a point onone wave to the samepoint on the next wave–“Crest to crest,” “troughto trough” or any otherequivalent points onadjacent waves• Unit of measure: meterGraph of displacementversus distance is a“snapshot” of the wave ata given time
Parts of the Wave• Equilibrium – rest position, zero movement• Crest – top of wave• Trough – bottom of wave• Amplitude – height from rest to top or bottom• Wavelength – distance wave travels in 1 cycle
Frequency• Frequency: number of cycles (repetitions)per unit of time (how often wave cycles)• f = 1/T (T = period)• Units: Hz (cycles/second)
Frequency (cont.)• The higherfrequency wavehas morecomplete cyclesin the sameamount of timeGraph of displacement versus timeshows the motion of a given position
Period (T)• Time for one complete wave to pass anygiven point• Unit of measure: seconds• The period and frequency are reciprocals:T = 1/ff = 1/T
Wave Speed (v)• How fast a wave transmits energy fromone place to another• IMPORTANT: Wave speed depends onlyon specific properties of the medium)• For example:– Wave in string: tension and density– Wave in fluid: rigidity and density– Wave in solid: elasticity and density• Constant for a given medium at givenconditions• Changes only if properties of medium do!• Unit of measure: meter/sec
Wave Speed (cont.)• Wave speeds vary widely:–Water waves: a few miles per hour–Sound (in air): about 340 m/sec or 1100ft/sec (depends on temperature)–Electromagnetic waves (in vacuum): about3.0 x 108meters/sec or 186,000 miles/sec• Speed of light in a medium is alwayslower than that in vacuum
Wave Speed, Frequency, andWavelength are Related• These variables are related through thefollowing equation:speed (m/s) = frequency (Hz) x wavelength (m)• Better: the product of f and λ is v• CAUTION: Remember: wave speed doesn’tdepend on f or λ; it depends on. . .v = f λthe properties of the medium it’straveling through!
Practice Problem• What does each letter represent,assuming that the x-axis is position?• What if the x-axis is time?A = wavelength; C and E = wavelength/2;D = amplitude; B = 2 x amplitudeA = period; C and E = period/2;D = amplitude; B = 2 x amplitude
What is the wavelength?How could you find the amplitude?
Practice Problem• Between what points would you measureto find the wavelength?x, mAnswers: A to E; B to F; C to G
Wave Properties (cont.)• Here’s an example transverse waveshowing some of the quantities we’vetalked about so far:How many complete wavelengths are shown?x, m2