Waves AP Physics

End Slide Definitions Wave – A disturbance in a given medium that carries energy from one place to another Medium – substance through which a wave travels; not all ways need mediums (plural: media) Pulse Wave – A single disturbance in a medium Continuous Wave – A set of disturbances occurring over and over usually in a pattern

What properties help describe a wave? Amplitude: the distance from the midpoint to the crest (or trough) of the wave. is the maximum displacement from equilibrium

Types of Waves Longitudinal Waves (Compressional) End Slide Types of Waves Longitudinal Waves (Compressional) Type of wave in which the medium vibrates in the same direction as the movement of energy Wave consists of a series of compressions and rarefactions Example: Sound

Types of Waves Transverse Waves End Slide Types of Waves Transverse Waves Type of wave in which the medium vibrates perpendicular to the movement of energy Wave consists of a series of crests and troughs Example: Light

Transverse vs. Longitudinal Waves

Types of Wave Surface Waves End Slide Types of Wave Surface Waves Type of wave in which the medium vibrates in a circular motion; a combination of up to down and side to side Example: Water waves

Wave Properties Wavelength – l (lambda) End Slide Wave Properties Wavelength – l (lambda) Distance in a wave between two like points, i.e. distance from compression to compression or from crest to crest Wavelength NOT Wavelength Wavelength

Wave Properties Period and Frequency End Slide Wave Properties Period and Frequency Period (T) – the amount of time it takes for one wave to pass Frequency ( f ) – the number of waves that pass in a second For Example…

15 Wavelengths in 5.0 sec. Time = 1.5 sec Time = 1.0 sec 14 4 5 3 2 1 13 6 11 12 7 10 9 8 Wavelengths 15 Wavelengths in 5.0 sec.

Period = = = Frequency = = = = Period and Frequency Time 5.0 sec End Slide Period and Frequency Time 5.0 sec Period = = # of Waves 15 waves = 0.33 sec # of Waves 15 waves Frequency = = 5.0 sec Time = = 3.0 1/sec 3 Hz

Wave Properties Period and Frequency End Slide Wave Properties Period and Frequency Frequency is the inverse of Period f = 1/T The unit for frequency is 1/sec or Hz (Hertz)

Wave Properties Speed of a Wave End Slide Wave Properties Speed of a Wave We know that Speed = how far / period of time. A wave will travel one wavelength in one period of time So, v = l/T Since f = 1/T, then … v = lf BTW, in college, you may see the Greek letter nu (n) used for frequency

Wave Properties Speed of a Wave (cont.) End Slide Wave Properties Speed of a Wave (cont.) The speed of a wave DOES NOT change unless the medium changes. i.e., for sound, temperature and pressure can change the speed of sound. The electro-magnetic fields can not be changed; so the speed of light will be constant. End Slide

Wave Properties Speed of a Wave (cont.) End Slide Wave Properties Speed of a Wave (cont.) Assuming a medium doesn’t change, what has to happen to the wavelength of a wave if you increase the frequency? Wavelength will decrease What has to happen to the frequency of a wave if you shorten the wavelength? Frequency will increase v = lf

End Slide Example #1 In music, the note B has a f = 247 Hz and a l = 1.34 m. What is the speed of these waves in air (a.k.a. sound)? v = lf = (1.34 m)(247 Hz) = 331 m*Hz = 331 m/s

End Slide Example#2 Suppose a planet is emitting a red light. Red light is known to have a wavelength of 7.00 x 10-7 m. Knowing the speed of light, what is the frequency of the light? f = v/l = (3.00 x 108 m/s)/(7.00 x 10-7 m) = 4.29 x 1014 Hz

Example #2 (cont.) For the previous example, End Slide Example #2 (cont.) For the previous example, f = 4.29 x 1014 Hz. What is the period of the red light? 𝐓 = 𝟏 𝒇 = 𝟏 𝟒.𝟐𝟗× 𝟏𝟎 𝟏𝟒 𝐇𝐳 = 2.33 x 10-15 sec

Wave Behaviors Superposition of Waves End Slide Wave Behaviors Superposition of Waves When two objects meet, they cannot occupy the same time and space; however, waves can pass through each other

Wave Behaviors Interference End Slide Wave Behaviors Interference If two waves are on the same side of the rest position, then the two waves will have constructive interference (add to each other)

Wave Behaviors Interference End Slide Wave Behaviors Interference If two waves are on opposite sides of the rest position, then the two waves will have destructive interference (subtract from each other)

Constructive Interference In constructive interference, the waves reinforce each other to produce a wave of increased amplitude.

Constructive Interference

Destructive Interference In destructive interference, the waves cancel each other and no wave is produced.

Wave Interference

Wave interference demo

Interference (different speed; same wavelength)

Interference – Beats (same speed; different wavelength)

Wave Behaviors Standing Waves End Slide Wave Behaviors Standing Waves A continuous wave that has points of no movement (nodes) and maximum movement (antinodes) Combination of reflections and interference

Measuring Speed Using Standing Waves End Slide Measuring Speed Using Standing Waves Measure Wavelength Count number of crests in a given time period; time for 10 crests? Divide 10 by that time to get frequency v = fl