Wave Phenomena Regents Physics Unit 7 I Basic

Wave Phenomena Regent’s Physics Unit 7

I. Basic Information • A. General – Waves are defined as a transfer of energy between two points. The wave may be seen or unseen – A light wave transfers energy from the sun to the earth – A water wave transfers energy across a body of water

General definitions of vibrations and waves • A vibration is anything that switches back and forth, to and fro, side to side, in and out, off and on, loud and soft, or up and down. A vibration is a wiggle in time. • A wave is a wiggle in both space and time. A wave extends from one place to another. • Waves are propagations of vibrations throughout space. • Waves transfer energy, not matter, from one place to another

B. Types of waves – Mechanical waves need a “medium” to travel through – Water waves, sound, or energy traveling through a spring or rope are examples of mechanical waves – Electromagnetic waves carry energy through the air at a high speed – Electromagnetic waves can’t be seen

Electromagnetic Waves • The following are classified as electromagnetic waves – light (the visible spectrum) – radio waves (fm and am) – Microwaves – Infrared radiation – x-rays – gamma radiation – ultraviolet Each of these waves travels at the same speed-3 x 108 m/s. They differ in how much energy they have

C. Classifying Waves • Waves are classified by the way they displace the medium or matter they move through • In a transverse wave, the medium or matter will move at a right angle to the direction of the wave movement of wave Particle movement

Wave Type Transverse Longitudinal

Continued • These diagrams will show what will happen to an object as a transverse wave moves through 1. object 2. 3.

Waves • The object moves up and down as the front passes, it does not move horizontally, nor does it gain or lose energy because of the wave • Water waves are classified as transverse • In a longitudinal wave, particles will vibrate in the same direction (parallel) as the wave • The wave will seem to “pass through” the object and have no effect on it • Sound waves and all electromagnetic waves are longitudinal in nature

D. Generating Waves • A wave front is defined as the leading edge of a newly created wave • If a stone is dropped in a pond, a wave pattern is produced wave front

Generating Waves • A circular series of transverse waves was produced as the stones’ energy is transferred to the water • The stone acted as a pulse, creating either a single wave or a series of waves • A continuous number of pulses will produce a series of regularly spaced waves, if the pulses continue indefinitely a standing wave is produced.

E. Standing Waves • Occur when a wave reflects upon itself and interference causes a pattern • Nodes remain stationary • Anti nodes-occur half way between nodes

Standing Waves Change the frequency in a standing wave and more nodes/antinodes appear in the event

F. Basic Wave Characteristics All waves have wave length, frequency and period, velocity, and amplitude 1. Wavelength • It is defined as the linear distance between the same points on consecutive waves • Since it is a distance it is measured in meters or cm Examples x y x= distance of 1 wavelength y= distance of ½ wavelength

Wave Properties Wavelength

2. Frequency • The number of waves, wave fronts, or pulses which pass a point in a given time (usually 1 sec) • Frequency is measured in waves/sec, termed a Hertz (Hz)

Wave Properties Frequency

Examples of Frequency • What is the frequency of the second hand of a clock? Frequency = 1 cycle/60 sec Period = 60 sec • What is the frequency of US Presidential elections? Frequency = 1 election/4 yrs Period = 4 yrs

3. Velocity • Defined as the speed a wave travels at • All electromagnetic waves have a speed of 3 x 108 m/s (c) • The speed of a sound wave in air is 330 m/s • The speed of all other waves can be calculated using this formula: V= f λ v=velocity f=frequency λ =wavelength

Velocity Continued • When dealing with electromagnetic waves the formula becomes: c=f λ c=3 x 108 m/s f=frequency λ =wavelength

Velocity • From this formula, you should note the following relationships among the variables: – As frequency or wavelength increases, velocity increases – As frequency decreases, wavelength increases

4. Period • Defined as the time required for one pulse, wave, or wave front to pass a given point • The formula is: T= 1/f T=period f=frequency Period is measured in seconds

Wave Properties Period

In symbolic form or

Sample Problem You are listening to your favorite Styx CD. You note that the sound waves have a pleasant frequency of 12 Hz. a. What is the velocity of the sound waves? b. What wavelength are the waves moving at? c. What are the waves period?

What determines the speed of a wave? (a) the frequency (b) the wavelength (c) the amplitude (d) the period (e) the medium of of transmission (e)

A skipper on a boat notices wave crests passing his anchor chain every 5 seconds. If the wave crests are 15 m apart, what is the speed of the water waves in m/s? (a) 5 (b) 15 (c) 75 (d) 10 (e) 3

What dictates the frequency of a sound wave? (a) wavelength (b) medium (c) source of the sound (d) speed (e) amplitude

5. Amplitude • Defined as the energy content a wave possesses • It also can be defined as a waves maximum displacement from its rest position • The highest point a wave reaches is called crest • The lowest point a wave reaches is called the trough

Wave Properties Amplitude

Sample Problem Compare waves A and B below in terms of the following properties: Amplitude Wavelength Frequency Wave A Wave B

For a medium transmitting a longitudinal wave, the areas of the medium where the density of the medium is temporarily increased are called. . . (a) rarefactions (b) compressions (c) density holes

II. Doppler effect, Interference, Reflection, and Refraction, and Diffraction A. The Doppler Effect • • Named after its discoverer, Christian Doppler, this phenomena deals with relative frequencies of sounds and other waves when people and objects are in motion More formally, the Doppler effect is defined as the change in the observed frequency of a wave when its source and the observer are in relative motion

DOPPLER EFFECT • Refers to the change in frequency when there is relative motion between an observer of waves and the source of the waves • Doppler with Sound

Examples • • Car horn pitch Train bells Police radar Each example works on the principal that because of the movement of an object or person, more waves will reach the person per second, increasing the perceived frequency of the wave

When you move away from a fixed source of sound, the frequency of the sound you hear. . . (a) is greater than what the source emits (b) is less than what the source emits (c) is the same as what the source emits

B. Wave Interference • Interference can occur if two waves traveling in the same media meet • The meeting of the waves is called a displacement • What effect the displacement has on the waves depends on the phase of the waves • Waves that are in phase have matching crests and troughs

Wave Interference When two wave pass each other their superposition causes reinforcement or cancellation.

Waves • Waves that are out of phase don’t have matching crests and troughs A set of waves “in phase” Although they differ in amplitude, these waves have similar wavelengths and frequencies

Waves A set of waves that is a ½ λ “out of phase” These waves share similar amplitudes, wavelengths, and frequencies, but are not matched “in phase”

destructive Waves • When waves are coming at each other they will meet and produce interference patterns • Waves that meet in phase will show constructive interference • Waves that meet out of phase will show destructive interference constructive

Constructive interference • Reinforcement when the crest of one wave overlaps the crest of another • Their individual effects adds together, resulting in a wave increased in amplitude

Crazy Waves! – The waves themselves are not changed because of the displacement. – Maximum constructive interference would occur if the waves met in phase. • 2. ) Destructive Interference • The waves combine to produce a pulse or wave with a smaller amplitude.

More on waves ( don’t you wish we were talkin’ about the ocean? ) … • Again, the waves themselves aren’t changed because of the displacement. • Maximum destructive interference will occur if the waves meet out of phase by ½ λ (a crest and trough meet) • The waves only cancel out if the crest and trough have equal amplitude.

Destructive Interference • Cancellation when crest of one wave overlaps trough of another reducing their individual effects • Water waves show these best • Out of phase- the crest of one wave arrives at a point at the same time as a trough of the second wave arrives, effects cancel each other • In phase- two waves crests and troughs arrive at a place at the same time, effects reinforce each other

Sound Wave Interference • Interference occurs when two sounds of difference frequency are heard superposed. • Constructive interference causes louder sound and destructive inference cause fainter sound. • This alternating pattern produces a beat. A piano tuners listens for beats to disappear.

Water Wave Interference • Left side is theoretical drawing of an interference pattern. • Right side is the actual interference pattern.

New Section!!!!! • E. Diffraction – Defined as the bending of waves around objects placed in their paths. – Again, this bending may cause a change in speed and/or wavelength, but it will not affect frequency.

More on Diffraction • Diffraction Patterns – When waves encounter barriers, diffraction occurs in such a way depending on how the wave reaches the barrier. – Examples include a single barrier, two barriers, or a double diffraction pattern

“Mirror on the wall…” (ok, not that kind of reflection) • C. Reflection – The property of reflection occurs when a wave hits a barrier that it can’t completely pass through – Part or all of the wave will bounce back, sometimes causing interference to take place. – Reflection may take place “head on” or at an angle

Angle of incidence and angle of reflection 1 2 Barrier

More Notes • 1 = the angle of incidence • 2 = the angle of reflection – The dashed line represents a normal, a line drawn perpendicular to the barrier that allows you to measure the angles – A special type of reflection, called inversion, will take place if a wave hits a very rigid barrier and undergoes a 180º phase change, this will produce a standing wave

Use your head • 1. ) Head on Wall

-=More lines=- Regular wave Inverted wave A standing wave is produced

A few little details… • When the wave reaches the wall, some of the amplitude (energy) will be absorbed by the wall, most however will bounce back. • Depending on the phase of the returning wave, constructive or destructive interference will take place.

In a different View- • 2. ) At an angle – When waves reach a barrier at an angle they will be reflected at the same angle at which they approached it. – More precisely, the angle of incidence is equal to the angle of reflection.

Ok guys, New Section • D. Refraction – The speed a wave travels at depends on the medium its traveling in. A wave may speed up or slow down depending on the type of medium the wave is entering. – Light waves will slow down as they travel from air to water. – When waves change medium their speed and wavelength will change, but their frequency WILL NOT. – You can calculate changes in speed and wavelength using the following proportion:

You can calculate changes in speed and wavelength using the following proportion: v 1 = v 2 λ 1 λ 2 v 1 = original speed λ 1 = original wavelength v 2 = new speed λ 2 = new wavelength

Put on your thinking caps!! Sample Questions • A youngster is making waves with her jump rope. She produces waves of wavelength 1. 2 m. The waves leave the rope and enter the air at a speed of 5 m/s. If the waves have a new wavelength of. 9 m, what was their original speed?

More Notes and Examples • Refraction is the property which describes a wave’s behavior change as it changes media. • Examples of medium changes that cause refraction – – 1. ) 2. ) 3. ) 4. ) Air to water Deep water to shallow water Thin rope to thick rope Air to a porous barrier

More Notes • Refraction causes a change in speed and wavelength, but does not effect frequency. • If a wave changes media at an angle, then the direction the refracted wave will move at will change.

Another New and Improved Section! • III. Sound Waves – Sound waves are classified as longitudinal waves. They share all properties of waves. – The frequency of sound waves is termed pitch. The higher the frequency, the higher the pitch. – The amplitude of sound waves is termed loudness. The greater the amplitude, the louder the sound. – The velocity of sound in air is approximately 330 m/s at 0°C. Changes in temp. will cause an increase or decrease in the sound wave’s speed.

There’s a lot more where this came from… • Reflected sound waves are called echo’s. Bats use reflected sound waves to locate objects. • Constructive interference of sound waves leads to richer sound, called stereo-maximum constructive interference is termed resonance. • Destructive interference can lead to dead areas where little or no sound is heard. • Sonic booms are caused when objects move faster than the waves they create, this causes constructive interference of sound waves as the object moves.

Sound Waves Molecules in the air vibrate about some average position creating the compressions and rarefactions. We call the frequency of sound the pitch.

Bow waves V-shaped pattern made by overlapping crest

Shock Waves Produced by supersonic aircraft, three-dimensional cone shaped Sonic boom – sharp crack heard when conical shell of compressed air that sweeps behind a supersonic aircraft reaches listeners on the ground below.

Supersonic

n. Subsonic - slower than the speed of sound • Supersonic Mach Number - faster than the speed of sound = speed of object speed of sound

Sonic booms from a plane are produced. . . (a) because the plane breaks through the sound barrier. (b) when the plane reaches the speed of sound. (c) by the plane traveling faster than the speed of sound. (d) by the plane traveling slower than the speed of sound.