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 Waves are everywhere in nature
What is a wave? • a wave is a disturbance that travels through a medium from one location to another. • a wave is the motion of a disturbance • waves transfer energy without the bulk transport of matter
Frequency and Period • Frequency measures the number of events that occur in a certain amount of time. • Period is the time to complete one cycle. • For example, if you get a paycheck twice a month, the frequency of payment is two per month (2 paychecks/month) and the period between checks is half a month.
Frequency (f)- the number of complete cycles per unit time f = cycles time measured in units of Hz (s-1) Eg. Five crests pass a point every second so f = 5 cycles/s = 5 Hz http://www.absorblearning.com/physics/demo/units/DJFPh064.html#Waveperiodandfrequency Period (T) - the shortest time interval during which the motion repeats itself T = time cycle measured in units of time (s, min) Eg. A pendulum bob takes 3.5 s to swoing “to and fro” f = 1/T T = 1/f & http://www.youtube.com/watch?v=t9HMTeHWi9c http://www.youtube.com/watch?v=Qa_KtWzmUpI&feature=related
Sample Problems e.g. A child on a swing completes 20 cycles in 25 s. Calculate the frequency and the period of the swing. e.g. A stroboscope is flashing so that the time interval between flashes is 1/80 s. Calculate the frequency of the stobe light’s flashes. e.g. Calculate the frequency and the period of a tuning fork that vibrates 24 000 times in 1.00 min. Page 10 #1 – 4, page 17 #8 - 13
Recall: a wave is a disturbance that travels through a medium from one location to another. A single disturbance is called a pulse or shock wave The slinky as a whole does not move forward, but its different parts move up and down about their mean positions. It is only the hump or the disturbance, which moves forward along the slinky.
TRANSVERSE The displacement of the particles of the medium isperpendicularto the direction of wave propagation (pulse). e.g. skipping ropes, radio waves, light waves, heat waves, stadium wave
Transverse Waves The stadium "wave" travels all around the stadium. None of the fans travel around the stadium. They only stand up and sit down. That means the movement of the medium (the people) transects (is perpendicular to) the movement of the wave making this a Transverse Wave!
LONGITUDINAL The displacement of the particles of the mediumisparallelto the direction of wave propagation (pulse). e.g. sound waves, tsunami waves, earthquake P waves
Longitudinal Waves The particles do not move down the tube with the wave; they simply oscillate back and forth about their individual equilibrium positions. http://www.youtube.com/watch?v=7cDAYFTXq3E&feature=related
SURFACE A combination of transverse and longitudinal. The particles move perpendicular and parallel to the pulse. e.g. water waves, Rayleigh earthquake waves http://www.youtube.com/watch?v=7yPTa8qi5X8
Anatomy of a Wave crest • 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
Anatomy of a Wave • 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. trough
Anatomy of a Wave cont. • The distance between the dashed line and point A (or point D, F or I) is called the Amplitude of the wave. • This is the maximum displacement that the wave moves away from its equilibrium. Amplitude
Anatomy of a Wave cont. wavelength • The distance between two consecutive similar points (in this case two crests) is called the wavelength (λ). • This is the length of the wave pulse. • Between what other points is can a wavelength be measured?
Recall: The distance between two consecutive similar points is called the wavelength (λ).
Phase Points along a transverse or longitudinal wave are said to be in phase if they are moving in the same direction and have the same amplitude.
Which other points are in phase with A? E, I. They are moving in the same direction AND have the same amplitude. Are C and G in phase with A? They are moving out of phase with A because they have the same amplitude but are moving in the OPPOSITE direction.
1. Give two examples of each of the three types of energy transfer. 2. What is the difference between a wave and a pulse? 3. Sharon is lying on a raft in a wave pool. Describe to Sharon, in terms of the waves she is riding, each of the following: amplitude, period, wavelength, speed, frequency. 4. For the wave pictured, a. measure the λ; b. measure the amplitude; c. state the number of positive pulses; d. name the type of wave; e. label two pulses that are in phase; f. label two pulses that are out of phase. 5. If you want to increase the amplitude of a pulse, what must you do to the amount of energy used to make the pulse? Practice: p. 17 – 18 #2, 3, 14, 16
Wave Speed • We can use what we know to determine how fast a wave is moving. What is the formula for velocity? • velocity = distance / time What distance do we know about a wave? • wavelength And what time do we know? • period
Wave Speed • v = / T andT = 1 / f • so we can also write v = f • velocity = frequency * wavelength • This is known as the wave equation. • Sample Problems: (in handout) • A wave coming in from the ocean has a wavelength of 0.080m. If the frequency of the wave is 2.5 Hz, what is its speed? • The distance between successive crests of water waves is 4.0m and the crests travel 9.0 m in 4.5 s. What is the frequency of the waves? What is the period? • Practice: p. 15 #1-6; p. 18 - 19 #15, 17-32
Wave Behavior • We know that waves travel through mediums. • But what happens when that medium runs out?
Boundary Behavior • 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.
Fixed EndReflection • One type of boundary that a wave may encounter is that it may be attached to a fixed end. • Fixed-end reflection occurs when a wave strikes a rigid barrier. • 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?
Fixed End Reflection • Here the incident pulse is an upward pulse. • The reflected pulse is upside-down. It is inverted. • A crest is reflected as a trough and vice versa. • The reflected pulse has the same speed, wavelength, and amplitude as the incident pulse. • A portion of the energy carried by the pulse is transmitted to the pole, causing the pole to vibrate.
Free EndReflection • 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?
Free EndReflection • If the reflection occurs at a free-end the reflected pulse is not inverted (erect). • 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.
Change in Medium • Our third boundary condition is when the medium of a wave changes. • Think of 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. • What will happen here?
Change in Medium • 1. Fast (thin) medium into a slow (thick) medium. • The slow medium acts as a barrier. • The transmitted pulse travels slower than the reflected pulse, is upright and has a shorter wavelength than the incident pulse. • The reflected pulse is inverted. • The speed & λ of the reflected pulse are the same as the speed and λ of the incident pulse
Change in Medium • Think of a thick rope attached to a thin 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. • What will happen here?
Change in Medium • 2. Slow (thick) medium into a fast (thin) medium • The fast medium does not act as a barrier. • The transmitted pulse is faster, is upright (erect) and has a longer wavelength than the incident pulse. • The reflected pulse is not inverted (it is erect). • The speed & λ of the reflected pulse are the same as the speed and λ of the incident pulse
Change in Medium Animation Check your understanding http://www.physicsclassroom.com/class/waves/u10l3a.cfm
Sample Problems • A negative pulse is sent along a spring. The spring is attached to a light thread that is tied to the wall. • Describe the speed and type of pulse that is transmitted at A. • Describe the speed and type of pulse that is reflected at A. • Describe the speed and type of pulse that is reflected at B. • A long spring runs across the floor of a room and out the door. A pulse is sent along the spring. After a few seconds, an inverted pulse returns. Is the spring attached to the wall in the room or is it lying loose on the floor? • You want to increase the wavelength of waves in a rope. Should you shake the rope with a high frequency or a low frequency? Should you send a pulse from a thin material into a thick material or send the pulse the other direction?
Practice: p. 17 #4 • LM: p. 3 - Reflection at Barriers
Laws of Reflection • The shape of a continuous crest or trough is called a wavefront. • If a wavefront hits a straight barrier, the wavefront is reflected back along the original path.
If the wavefront hits a straight barrier at an angle (angle of incidence), the wavefront is reflected at an angle (angle of reflection). • The angles are measured from the normal, a line that is perpendicular to the barrier.
If the wavefront approaches a parabolic barrier, the waves are reflected to a point called the focal point. • The normal of a parabolic reflector is perpendicular to the tangent (normal) at that point.
Sample Problems • The diagram shows wave fronts striking a barrier. • Draw the incident direction. • Draw the normal. • Measure the angle of incidence. • Draw the reflected direction. • Draw the reflected wave fronts.
2. The diagram shows the direction of a wave that strikes a curved barrier. • Draw the tangent line. • Draw the normal. • Measure the angle of incidence. • Draw the reflected direction. • Draw the reflected wave fronts.