Wave Review

If a vibrational disturbance occurs, energy travels/propagates out in all directions from the vibrational source. 1 disturbance = pulse

Oscillators generate continuous waves Many pulses = continuous wave.

Traveling waves (as opposed to standing waves) transfer energy! Matter is not transferred by waves Give example of how we know E gets transferred.

Wave Vocabulary Points in Phase. 1 cycle passes in time = 1 period crests Equilibrium Points in Phase. 1 cycle passes in time = 1 period f = cycles passing per sec Hz Medium – matl wave travels through.

1. The wave below shows a “snapshot” that lasted 4. 0 seconds 1. The wave below shows a “snapshot” that lasted 4.0 seconds. What is the frequency of the wave? 4.0 seconds 2 cycles/4 s = 0.5 Hz

Transverse Waves Earthquake S waves, EM waves.

Longitudinal/Compressional Particles compressed and expanded parallel to energy propagation. Compressions – high P, density Rarefactions- low P, density. Sound.

All points on a wave that are in phase comprise a wave front.

Rays – a ray is an arrow sketched through the wave fronts (perpendicular) to show direction of wave propagation.

Wave Speed Speed/Velocity = d/t If a crest (or any point on a wave) moves 20m in 5 sec, v = 20m/5s = 4 m/s. Waves of the same type travel through homogenous materials at same speed regardless of frequency of wavelength.

Relationship of wave speed to wavelength(l) and frequency(f). v = d/t Relationship of wave speed to wavelength(l) and frequency(f). v = d/t but for waves d = 1l occurs in time T (1period) so v = l/T since freq f =1/T v =lf

2. A machine gun fires 10 rounds/sec at 300 m/s. a 2. A machine gun fires 10 rounds/sec at 300 m/s. a. What is the distance between the bullets? b. What would happen to the distance if the firing rate were increased. f = 10 Hz. v = 300 m/s. l = ? v = fl. l = 300 m/s / 10 s-1. l = 30 m.

v = l f. Wave Speed Depends on medium Fixed by source oscillation Depends on the others.

What can happen when wave pulses or continuous waves interact? Transmission Superposition & Interference

What happens when they pass?

Superposition – combining & addition of waves.

Wave Superposition/Interference Destructive Constructive

Boundary Behavior Transmission (partial or not at all), Reflection (partial or total) Refraction – transmission with velocity change. Diffraction – bending around boundary.

Wave hits rigid boundary: Reflection – pulse inverts. It comes back totally opposite.

Pulse hits soft boundary?

Law of reflection

Refraction – D speed and bending upon entering new material Refraction – D speed and bending upon entering new material. The frequency is fixed by source. Constant speed until new material.

Wavefronts entering new material

Diffraction – curvature through small openings (apertures) or around obstacles.

Curvature vs. Opening width

Diffraction around obstacle.

Never a frequency change unless the vibration rate of source changes. Or --

Object & observer are in relative motion.

Types of Waves Mechanical Non-mechanical Medium No medium

Examples? Compressional/ pressure/ longitudinal Always mechanical. Why? Examples?

Transverse Examples?

Polarization Transverse Waves

Wave speed Deduce that for waves v = lf.

t but for waves d = 1l occurs in time T v = d t but for waves d = 1l occurs in time T v = l/T since freq f =1/T v =lf

d – time graph 1 point in oscillatory motion See hamper transverse.

See hamper longitudinal pg 91. Displ – position graph shows the displacement of every point on wave at a given time. Need to see equilibrium position. See hamper longitudinal pg 91.

IB Set IB Wave Prac 1 Read hamper 4.4

Frequency and Amplitude Physical Properties

For light increased amplitude increases brightness.

For sound: increased amplitude increases volume.

Wave frequency (f, l) Wave type for EM waves. Color for light. Sound = f pitch

Doppler Effect Objects in relative motion: toward each other – frequency increases (l decreases). away – frequency decreases (l increases).

Doppler Red/Blue Shift galaxies and stars.

Sound

Sound velocity solid liquid gas In gas hot faster. cold slower. Increasing velocity

Resonance & Sympathetic Vibration

All objects have a natural frequency of vibration. Resonance - the inducing of vibrations of a natural rate by a vibrating source having the same frequency “sympathetic vibrations” System resonance – amplitude will increase.

Push at natural frequency, amplitude increases

Standing Waves - No net E transfer. Fixed pattern of constructive/destructive interference.

Standing Wave patterns form notes Standing Wave patterns form notes. Each string or pipe vibrates or resonates with particular f of standing waves. Other frequencies tend to die out.

Standing waves can arise when the reflected waves interfere constructively with the incident waves causing the amplitude to increase.   The resonance is created by constructive interference of two waves which travel in opposite directions in the medium, but the visual effect is that of an entire system moving in SHM.

A broad variety of tone colors exist because most sounds we perceive as pitch contain many frequencies. The predominant pitch is called the fundamental frequency. It is the longest l that forms a standing wave.

Although we would perceive a string vibrating as a whole, it vibrates in a pattern that appears erratic producing many different overtone pitches. What results are particular tone colors or timbres of instruments and voices.

Waveform with overtones.

Frequencies which occur along with the primary note are called the harmonic or overtone series. When C is the fundamental the pitches below represent its first 15 overtones.

Harmonics There are several standing waves which can be produced by vibrations on a string, or rope. Each pattern corresponds to vibrations which occur at a particular frequency and is known as a harmonic.

The lowest possible frequency at which a string could vibrate to form a standing wave pattern is known as the fundamental frequency or the first harmonic.

2nd Harmonic

Which One??

String Length L, l & Harmonics Standing waves can form on a string of length L, when the l can = ½ L, or 2/2 L, or 3/2L etc. Standing waves are the overtones or harmonics. L = nln. n = 1, 2, 3, 4 harmonics. 2

form if ½ l can fit the string or pipe exactly. To calculate: Harmonic Frequencies form if ½ l can fit the string or pipe exactly. To calculate: Substitute v/f for l.

1st standing wave forms when l = 2L First harmonic frequency is when n = 1 as below. When n = 1 f is fundamental frequency or 1st harmonic.

For second harmonic n = 2. f2 = v/L Other standing waves with smaller wavelengths form other frequencies that ring out along with the fundamental. For second harmonic n = 2. f2 = v/L

In general, The harmonic frequencies can be found where n = 1,2,3… and n corresponds to the harmonic. v is the velocity of the wave on the string. L is the string length.

The d between anti & nodes on a standing wave is ½ l.

Pipes and Air Columns

closed-pipe resonator A resonant air column is simply a standing longitudinal wave system, much like standing waves on a string. closed-pipe resonator tube in which one end is open and the other end is closed open-pipe resonator tube in which both ends are open

Open Pipe – open end has antinode.

Standing Waves in Open Pipe Both ends must be antinodes Standing Waves in Open Pipe Both ends must be antinodes. How much of the wavelength is the fundamental?

The 1st harmonic or fundamental can fit ½ l into the tube. Just like the string L = nl 2 fn = nv 2L Where n, the harmonic is an integer.

Closed pipes must have a node at closed end and an antinode at the open end. How many wavelengths??

Here is the next harmonic. How many l’s?

There are only odd harmonics possible. L = 1/4l. L = 3/4l. L = 5/4l. fn = nv where n = 1,3,5 … 4L

Mech Universe Waves.

Practice Review set