Vibrations Back and Forth Motion (“Oscillations” in Time)

• Properties of Vibration:Period (time for a full cycle): TFrequency (number of cycles per second): f =1/TAmplitude: A = Maximum displacement from

equilibriumVelocity: v = velocity of mass going back and

forth. • Where is it greatest?• Where is it least?

Wave Motion• Oscillation in Time and Space.

Freezing time: See oscillation over spaceLook at one point: See oscillations over time.

Waves carry Energy.

If the water only moves up and down, what is “carried” by the wave?

Some Characteristics of Waves

• Amplitude (A)Maximum “displacement” from equilibriumLight Waves (“Electric and Magnetic fields”) Sound: (high pressure/density areas)

• Intensity (I ~ A2 ~ Power)

(“~” means proportional to)Light Wave: BrightnessSound Wave: LoudnessSO: Is “negative amplitude” loud (or soft), bright

(or dim)?

More Characteristics of Waves• Period (T) (s)

Time between successive crests (looking at one point in space)

• Frequency (f) (Hertz (“Hz" or 1/s))Number of crests passing a point per second.Light: color: Higher f means bluer, Lower f means

redder.Sound: pitch: Higher f means higher pitch.

• Wavelength (λ) (m)Distance between successive crests (time frozen)

• Velocity (v = f λ) (m/s)Velocity at which energy is carried.

Types of Waves

• Transverse WavesAmplitude is

perpendicular to velocity of wave.

Waves in strings, Light Waves

• Longitudinal WavesAmplitude is parallel to

velocity of wave.Sound Waves, parallel

compression of springs, Follow any one particle

in the animation; it oscillates in time.

Period or Wavelength?(watch what’s plotted on horizontal axis)

How Do Waves Interact? Interference

• When two waves pass through the same region at the same time:they interfere with each other to create

a new shape.Constructive Interference: Crest meets

crest, trough meets trough. (Max Brightness or Loudness)

Destructive Interference: Crest meets Trough (Max Darkness or Silence)

• Intermediate shapes depend on wave properties.

Self-Interference and Standing Waves

• A wave hitting a wall can Reflect and Interfere with its reflection

• ResonanceAt certain frequencies MAXIMUM constructive

interference occurs.Amplitudes vibrate up and down (at “antinodes”)Fixed points of zero amplitude occur (at “nodes”)Waves appear to stand still; energy flow is zero

(flow to right = flow to left)Applet and Illustrations for Standing Waves on String

sThese are “natural” or “resonant” frequencies.

Standing Waves on a String

• For waves on a string traveling along length (L) between two fixed ends, to form standing waves:Displacement = 0 at ends requires:Integer number of half wavelengths must fit on L.OR: (n = integer: 1, 2, 3, ….) L = n (λn/2)

• Allowed wavelengths: or λn = (2L)/n

• Natural Frequencies: Get from: fn = v/λn

• First Frequency is called the “First Harmonic”: f1

• Second Harmonic n=2: f2 = 2f1

• And so on: nth Harmonic: fn = n f1

Applet and Illustrations for Standing Waves on Strings

Resonance in Sound Waves

• Send a sound wave down a pipe of length (L) closed at one end.It reflects off the closed end (where

displacement is zero).And interferes with the incoming

wave.Resonance: Maximum Loudness

occurs when we have maximum amplitude at open mouth:

Ln = n λ/4 for n=1,3,5, ..

• For n=1: L = λ/4 or λ = 4LBut v = λf = 4Lf = speed of soundLet’s measure it.

Resonance in Vibrations

• A vibrating object has a “natural” frequency at which it likes to vibrate.Example we’ve seen: Pendulumf = 1/T

• If we “drive” the pendulum at its natural frequency, its amplitude gets very large.Ex1: A parent pushing a child on a swing.Ex2: Here’s a pendulum. Let’s:

• Measure its natural frequency with a stopwatch• Then “drive” it at its natural fequency.

The Doppler Effect

How does our perception of a wave change when its source is moving towards us or away from us?

Sound Wave AppletIf the relative motion of the source is towards us we

perceive higher frequency (higher pitch or bluer).If the relative motion of the source is away from us

perceive lower frequency (lower pitch or redder).The observed shift in frequency is called the “Doppler

Shift”.

What if a source of sound moves as fast as the sound wave itself?

• The source will move with the wave itself.• Both source and wave arrive at our ear at the

same time. Sound Wave Applet• We hear all of the amplitudes compressed

together (LOUD) at one instant (SUDDEN)It’s a “SONIC BOOM”

• What if the source exceeds speed of sound?Source arrives before the sound it makes. We don’t

hear it until it’s past us.A “CONICAL SHOCK WAVE”.

A Plane in Supersonic Flight

The Doppler Shift also tells us….

• Whether a storm system is coming to us or not.By bouncing radio waves off rain droplets and

analyzing the shift between sent and received waves.

• Whether we’re exceeding the speed limit.By bouncing radio waves off your car (RADAR)

• Whether we have blood clots in our legs or the rate of blood flow through our hearts.By bouncing sound waves off red blood cells.

• Whether or not the Universe is expanding.What does that mean?