Waves. Sec Wave Properties. Waves are everywhere in nature. What is a wave? Example: Slinky Wave

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1 Waves PART I Wave Properties Wave Anatomy PART II Wave Math Wave Behavior PART III Sound Waves Light Waves (aka Electromagnetic Waves or Radiation) 1 Sec Wave Properties Objectives Identify how waves transfer energy without transferring matter. Contrast transverse and longitudinal waves. Relate wave speed, wave-length, and frequency. 2 PART I Wave Properties Wave Anatomy GOALS: What is a wave? What are the different types of waves? What are the parts of a wave? Waves are everywhere in nature Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, telephone chord waves, stadium waves, earthquake waves, waves on a string, slinky waves 3 4 What is a wave? a wave is a disturbance pattern that travels through a medium. Waves carry energy Example: Slinky Wave Slinky is the medium (steel) the wave is the disturbance traveling through it the wave carries energy through the medium 5 6 1

2 Medium 2 Types of Wave: = the substance that the wave travels through Wave Medium Water Wave Water Sound Wave Air Slinky Wave Steel Stadium Wave People 7 8 Transverse Wave: Longitudinal (Compression) Wave 9 Transverse Wave: *denser medium will slow wave down Longitudinal (Compression) Wave *denser medium will speed wave up Medium moves perpendicular to direction of wave energy Medium moves parallel to direction of wave energy 10 Math Longitudinal (Compression) Waves This slinky wave is a longitudinal (compression) wave in which steel is the medium. A sound wave is a longitudinal (compression) wave in which air is the medium

3 Transverse Waves: Wave moves forward Medium moves up and down Longitudinal (Compression) Waves: Wave moves forward Medium moves side to side What moves where? Surface Waves Combination of both longitudinal and transverse. Longitudinal at depth; Transverse at surface Anatomy of a Wave We will use a transverse wave to describe this since it is easier to see the pieces. Wave Anatomy: Compression Wave as a Transverse Wave Link: 15 What about longitudinal waves? 16 Anatomy of a Continuous Wave Anatomy of a Wave crest In our wave here the dashed line represents the equilibrium position. (origin) Once the medium is disturbed, it moves away from this position and then returns to it 17 The points A and F are called the CRESTS of the wave. This is the point where the wave exhibits the maximum amount of positive or upwards displacement 18 3

4 Anatomy of a Wave Anatomy of a Wave Amplitude trough The points D and I are called the TROUGHS of the wave. These are the points where the wave exhibits its maximum negative or downward displacement. 19 The distance between the dashed line and point A is called the Amplitude of the wave. This is the maximum displacement that the wave moves away from its origin. 20 Anatomy of a Wave wavelength Drawing Waves The distance between two consecutive similar points (in this case two crests) is called the wavelength. This is the length of the λwave pulse. Between what other points is can a wavelength be measured? λ Wave Anatomy: Summary (Later we ll add nodes and antinodes) Anatomy of a Wave What else can we determine? Remember; Waves move, and the medium moves to, over time The words period and frequency take the passage of time into account

5 Period and Frequency wavea.htm PART II: Wave Math Wave Behavior PART II Wave Math GOALS: How can we describe wave motion? How can we predict wave motion? Period ( T ): = The amount of time it takes for one wave to pass a point Units: seconds (s) Frequency ( ): = Waves per second (How many waves pass by a point per second) Units: Hertz (Hz) 27 1 Hertz = 1wave per second 28 Period and Frequency are related = 1/T = (# of waves passed) / (time passed) T= 1/ 29 Wave frequency Frequency measures how often something happens over a certain amount of time. We can measure how many times a wavelength passes a point per second, and this will give us the frequency. 30 5

6 Wave frequency Suppose I wiggle a slinky back and forth, and count that 6 waves pass a point in 2 seconds. What would the frequency be? 6 waves / 2 second 3 waves / 1 second = 3 Hz Remember: Hertz (Hz) means waves per second. Wave Period The period is the time it takes for one wave to pass by. If there are 3 waves per second, then one wave only takes a third of a second. T = f = 3 T = 1 / f f = 1 / T = 1 / 3 = 1 / Period and Frequency A continuous wave is traveling so fast that a crest passes by one point every 0.5 seconds. What is the frequency of the wave? What is the period of the wave? Wavelength ( ) The distance from the crest of one wave to the crest of the next or from the trough of a wave to the next trough wave speed or velocity ( ) Different waves travel at different speeds. There is a relationship between speed, wavelength and frequency. The Wave Equation: v f = Wave speed or velocity (m/s) = Wavelength (m) = Frequency (Hz)

7 v f v f What is the frequency of a wave if it has a speed of 12 cm/s and a wavelength of 3 cm? (12 cm/s) / (3cm) = 4 Hz A wave has a frequency of 5 Hz and a wave speed of 18 m/s. What is it s wavelength? (18 m/s) / (5 Hz) = 3.6 m The frequency is 4 waves per second Remember: Hertz means waves per second 37 The wavelength is 3.6 meters. 38 Wave Behavior: Boundaries Wave Behavior: Boundaries The behavior of a wave when it reaches the end of its medium is called the wave s BOUNDARY BEHAVIOR. When one medium ends and another begins, that is called a boundary. Boundaries change speed and wavelength Frequency stays the same Type of barrier determines type of change Wave Behavior: Boundaries Fixed End The wave before it hits the boundary is called the INCIDENT WAVE. Sometimes the energy may be reflected backwards as a REFLECTED WAVE. The wave energy that continues into the new medium is called the TRANSMITTED WAVE. 41 One type of boundary that a wave may encounter is that it may be attached to a fixed end. In this case, the end of the medium will not be able to move. What is going to happen if a wave pulse goes down this string and encounters the fixed end? 42 7

8 Fixed End Fixed End Reflection Here the incident pulse is an upward pulse. The reflected pulse is upside-down. It is inverted. The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse. 43 When a wave enters a more dense or rigid medium, the boundary acts as a fixed end boundary, and produces fixed end reflection: the reflected wave is inverted. 44 Free End Free End Another boundary type is when a wave s medium is attached to a stationary object as a free end. In this situation, the end of the medium is allowed to slide up and down. What would happen in this case? 45 Here the reflected pulse is not inverted. It is identical to the incident pulse, except it is moving in the opposite direction. The speed, wavelength, and amplitude are the same as the incident pulse. 46 Free End Animation Change in Medium When a wave enters a less dense or less rigid medium, the boundary acts as a free end boundary, and produces free end reflection: the reflected wave is not inverted

9 Change in Medium Change in Medium A change in medium is a type of boundary. Consider a thin rope attached to a thick rope. The point where the two ropes are attached is the boundary. At this point, a wave pulse will transfer from one medium to another. In this situation part of the wave is reflected, and part of the wave is transmitted. Part of the wave energy is transferred to the more dense medium, and part is reflected. The transmitted pulse is upright, while the What will happen here? reflected pulse is inverted. Change in Medium Change in Medium Animation The speed and wavelength of the reflected wave remain the same, but the amplitude decreases. The speed, wavelength, and amplitude of the transmitted pulse are all smaller than in the incident pulse Wave Behavior: Interference and Superposition Constructive Interference Let s consider two waves moving towards each other, both having a positive upward amplitude. What will happen when they meet? or

10 Constructive Interference They will ADD together to produce a greater amplitude. This is known as CONSTRUCTIVE INTERFERENCE. Destructive Interference Now let s consider the opposite, two waves moving towards each other, one having a positive (upward) and one a negative (downward) amplitude. What will happen when they meet? Destructive Interference Occurs when the crests of one wave and the Interference troughs of another wave overlap Destructive Interference This time when they meet they will produce a smaller amplitude. This is know as DESTRUCTIVE INTERFERENCE Interference SIM Here s what it looks like:. SIM - Interference (SIM1) (SIM2)

11 Interference is Everywhere Complex interference patterns in sound waves make up complex sounds and noises. Constructive interference: Waves are In Phase Crest lines up with crest Amplitudes Add Destructive interference: Waves are Out of Phase Crest and Trough line up Amplitudes Cancel Out Interference Constructive - waves add in phase, producing larger peaks than any wave alone. Destructive - waves add out of phase, producing smaller peaks than a single wave alone. Check Your Understanding Which points will produce constructive interference and which will produce destructive interference? Constructive G, J, M, N Destructive H, I, K, L, O Beating Frequency (SIM1) (SIM2) 65 11