Waves Waves and Wave Properties Serway Ch. 13: Section 8 thru 13 www.archive.org Physics B Lesson 42: Wave Basics Mechanical Caused by vibrations in a medium Examples: Sound Waves in a string Water waves Earthquakes Electromagnetic Caused by fluctuating electric and magnetic fields Examples: Light Radio Types of Waves 1
Electromagnetic versus Mechanical Waves Another way to categorize waves is on the basis of their ability or inability to transmit energy through a vacuum (i.e., empty space). All waves transmit (carry) energy and momentum. Can a scream be heard in space? 2
Electromagnetic Waves An electromagnetic wave is a wave that is capable of transmitting its energy through a vacuum. Electromagnetic waves are produced by the vibration of charged particles. Mechanical Waves A mechanical wave is a wave that is not capable of transmitting its energy through a vacuum. Mechanical waves require a medium in order to transport their energy from one location to another. 3
Mechanical Waves A mechanical wave is a disturbance which propagates through a medium with little or no net displacement of the particles of the medium. Sound Wave Water Waves Wave Pulse People Wave Categories of Waves Longitudinal Transverse Surface What type of wave is this one? 4
Transverse Waves A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves. Example: Waves on a String Longitudinal Waves A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. These are also called compression waves. Example: Sound 5
Longitudinal Waves Surface Waves A surface wave is a wave in which particles of the medium undergo a circular or elliptical motion. Surface waves are neither longitudinal nor transverse. In a surface wave, it is only the particles at the surface of the medium that undergo the motion. Example: Ocean waves (at the surface) 6
General Wave Properties Parts of a Transverse Wave 3 λ: wavelength (m) crest equilibrium A: amplitude (m) 2 4 6 x(m) -3 y(m) trough 7
Speed of a Wave The speed of a wave is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. The speed depends strictly on the medium s properties in particular it s density. Recall the speed of an object: d v = t Where, d: distance (m) t: time (s) The speed of a wave: v = fλ Where, v : speed (m /s) λ : wavelength (m) ƒ : frequency (s 1, Hz) Period The time taken for one full oscillation. 1 T = f Where, T - period (s) ƒ -frequency (s -1, Hz) 8
General Wave Behavior What happens to waves when they collide? SUPERPOSITION & INTERFERENCE 9
Principle of Superposition When two or more waves pass a particular point in a medium simultaneously, the resulting displacement at that point in the medium is the sum of the displacements due to each individual wave. The waves interfere with each other. Types of interference. CONSTRUCTIVE INTERFERENCE If the waves are in phase, that is crests and troughs are aligned, the amplitude is increased. DESTRUCTIVE INTERFERENCE If the waves are out of phase, that is crests and troughs are completely misaligned, the amplitude is decreased and can even be zero. 10
Constructive Interference crests aligned with crest waves are in phase Constructive Interference 11
Destructive Interference crests aligned with troughs waves are out of phase Destructive Interference 12
What happens to a wave at the interface of two media (boundary)? BOUNDARY BEHAVIOR Reflection of waves Occurs when a wave strikes a medium boundary and bounces back into original medium. Completely reflected waves have the same energy and speed as original wave. 13
Reflection Types Fixed-end reflection: The incident pulse reflects with inverted phase. A portion of the energy carried by the pulse is reflected and returns towards the left end of the rope. The disturbance that returns to the left after bouncing off the boundary is known as the reflected pulse. A portion of the energy carried by the pulse is transmitted to the other medium/boundary. The speed of the reflected pulse is the same as the speed of the incident pulse. The wavelength of the reflected pulse is the same as the wavelength of the incident pulse. The amplitude of the reflected pulse is less than the amplitude of the incident pulse. Reflection Types Free-end reflection: The wave reflects with the same phase The reflected pulse is not inverted. It is also displaced upward. Difficult to observe the behavior (think of the slinky lab)/ 14
Across a Boundary from Less to More Dense Reflected pulse. Transmitted pulse. The transmitted pulse (in the more dense medium) is traveling slower than the reflected pulse (in the less dense medium). The transmitted pulse (in the more dense medium) has a smaller wavelength than the reflected pulse (in the less dense medium). The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse. Across a Boundary from More to Less Dense The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium). The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium). The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse. 15
Refraction of waves Transmission of wave from one medium to another which involves a change in the direction of waves as they pass into another medium. Refracted waves may change speed and wavelength. Refraction is almost always accompanied by some reflection. Refracted waves do not change frequency. Depth of water Animation courtesy of Dr. Dan Russell, Kettering University Diffraction of waves Involves a change in direction of waves as they pass through an opening or around a barrier in their path. The amount of diffraction increases with increasing wavelength. Example: Water waves have the ability to travel around corners, around obstacles and through openings. Sound can be heard around corners. 16
Reflection, Refraction, & Diffraction All are boundary behaviors of waves associated with the bending of the path of a wave. Reflection: Occurs when there is a bouncing off of a barrier Refraction: The change in direction of waves that occurs when waves travel from one medium to another. Diffraction: The bending of waves around obstacles and openings. More Wave Behavior 17
Doppler Effect The Doppler effect causes the received frequency of a source (how it is perceived when it gets to its destination) to differ from the sent frequency if there is motion that is increasing or decreasing the distance between the source and the receiver Same f Low f High f Doppler Effect (light) Doppler effect also affects the light emitted by other bodies in space. Described with colors rather than frequency. Blue shift an object s its light waves are compacted and it is coming towards us. Red shit - the light waves are spread apart, and it is traveling away from us. All other stars we have detected are "red shifted," evidence for the big bang theory (that the universe is constantly expanding). 18
Doppler Effect (sound) The Doppler Effect is the raising or lowering of the perceived pitch of a sound based on the relative motion of observer and source of the sound. Lower f Higher f http://newton.umsl.ed u/exhibit/doppler.au Detector Source Detector When a car blowing its horn races toward you, the sound of its horn appears higher in pitch, since the wavelength has been effectively shortened by the motion of the car relative to you. The opposite happens when the car races away. Doppler Effect & Sound Barrier Stationary Source Source moving with v source < v sound ( Mach 0.7 ) 19
Doppler Effect & Sound Barrier Source moving with v source = v sound (Mach 1 - breaking the sound barrier) Source moving with v source > v sound (Mach 1.4 - supersonic) Standing Waves 20
Standing Wave A standing wave is a wave which is reflected back and forth between fixed ends (of a string or pipe, for example). Reflection may be fixed or open-ended. Superposition of the wave upon itself results in a pattern of constructive and destructive interference and an enhanced wave. Strings: http://www.walter-fendt.de/ph14e/stwaverefl.htm Pipes: http://www.physics.smu.edu/~olness/www/05fall1320/ap plet/pipe-waves.html Standing Waves NODES: points along the medium that appear to be standing still, also referred to as points of no displacement, are referred to as nodes. ANTINODES: points along the medium that undergo vibrations between a large positive and large negative displacement. These points undergo the maximum displacement during each vibrational cycle of the standing wave A standing wave pattern always consists of an alternating pattern of nodes and antinodes. 21