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Waves. Overview (Text p382>). Waves – What are they?. Imagine dropping a stone into a still pond and watching the result. A wave is a disturbance that transfers energy from one point to another in wave fronts. Examples Ocean wave Sound wave Light wave Radio wave .

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waves

Waves

Overview

(Text p382>)

waves what are they
Waves – What are they?
  • Imagine dropping a stone into a still pond and watching the result.
  • A wave is a disturbance that transfers energy from one point to another in wave fronts.
    • Examples
      • Ocean wave
      • Sound wave
      • Light wave
      • Radio wave
waves basic characteristics
Waves – Basic Characteristics
  • Frequency (f) cycles/sec (Hz)
  • Period (T) seconds
  • Speed (v) meters/sec
  • Amplitude (A) meters
  • Wavelength () meters
  • Peak/Trough
  • Wave spd = w/length * freq
    • v =  * f
wave types
Wave Types
  • 2 types of waves:
    • Electromagnetic
      • Require NO medium for transport
      • Speed is speed of light @ 3 x 108 m/s
      • Examples – light, radio, heat, gamma
    • Mechanical
      • Require a medium for transport of energy
      • Speed depends on medium material
      • Examples – sound, water, seismic
waves electromagnetic
Waves – Electromagnetic
  • Wave speed is 3 x 108 m/s
  • Electric & Magnetic fields are perpendicular
waves radio
Waves – Radio
  • Electromagnetic type
  • Most radio waves are broadcast on 2 bands
    • AM – amplitude modulation (550-1600 kHz)
      • Ex. WTON 1240 kHz
    • FM – frequency modulation (86 – 108 MHz)
      • Ex. WMRA 90.7 MHz
    • What are their respective wavelengths?
practice
Practice
  • What is the wavelength of the radio carrier signal being transmitted by WTON @1240 kHz?
  • Solve c = λ*f for λ.
    • 3e8 = λ * 1240e3
    • λ = 3e8/1240e3 = 241.9 m
practice1
Practice
  • What is the wavelength of the radio carrier signal being transmitted by WMRA @ 90.7 MHz?
  • Solve c = λ*f for λ.
    • 3e8 = λ * 90.7e6
    • λ = 3e8/90.8e6 = 3.3 m
mechanical waves
Mechanical Waves
  • 2 types of mechanical waves
    • Transverse
      • “across”
    • Longitudinal
      • “along”
waves mechanical transverse
Waves – Mechanical Transverse
  • Transverse
    • Particles move perpendicularly to the wave motion being displaced from a rest position
      • Example – stringed instruments, surface of liquids

>> Direction of wave motion >>

waves mechanical longitudinal
Waves - Mechanical Longitudinal
  • Particles move parallel to the wave motion, causing points of compression and rarefaction
    • Example - sound

>> Direction of wave motion >>

sound
Sound
  • Speed of sound in air depends on temperature
    • Vs= 331 + 0.6(T) above 0˚C
      • Ex. What is the speed of sound at 20°C?
        • Ss = 331 + 0.6 x 20 = 343 m/s
  • Speed of sound also depends upon the medium’s density & elasticity. In materials with high elasticity (ex. steel 5130 m/s) the molecules respond quickly to each other’s motions, transmitting energy with little loss.
    • Other examples – water (1500), lead (1320) hydrogen (1290)

Speed of sound = 340 m/s (unless other info is given)

sounds and humans
Sounds and humans
  • Average human ear can detect & process tones from
    • 20 Hz (bass – low frequencies) to
    • 20,000 Hz (treble – high frequencies)
doppler effect
Doppler Effect
  • What is it?
    • The apparent change in frequency of sound due to the motion of the source and/or the observer.
doppler effect1
Doppler Effect
  • Moving car example
doppler effect formula
Doppler Effect Formula
  • f’ = apparent freq
  • f = actual freq
  • v = speed of sound
  • vo = speed of observer (+/- if observer moves to/away from source)
  • vs = speed of source (+/- if source moves to/away from the observer)
  • Video example
sound barrier 2
Sound Barrier #2

THRUST SSC

LSR: 763 mph or 1268 km/hr

doppler practice
Doppler Practice
  • A police car drives at 30 m/s toward the scene of a crime, with its siren blaring at a frequency of 2000 Hz.
    • At what frequency do people hear the siren as it approaches?
    • At what frequency do they hear it as it passes? (The speed of sound in the air is 340 m/s.)
doppler practice1
Doppler Practice
  • A car moving at 20 m/s with its horn blowing (f = 1200 Hz) is chasing another car going 15 m/s.
    • What is the apparent frequency of the horn as heard by the driver being chased?
interference of waves
Interference of Waves
  • 2 waves traveling in opposite directions in the same medium interfere.
  • Interference can be:
    • Constructive (waves reinforce – amplitudes add in resulting wave)
    • Destructive (waves cancel – amplitudes subtract in resulting wave)
  • Termed - Superposition of Waves
superposition of waves1
Superposition of Waves

Special conditions for amp, freq and λ…

standing wave
Standing Wave?
  • A wave that results from the interference of 2 waves with the same frequency, wavelength and amplitude, traveling in the opposite direction along a medium.
  • There are alternate regions of destructive (node) and constructive (antinode) interference.
basic terms
Basic Terms
  • Harmonic number
    • n (1st, 2nd, 3rd, …)
  • Fundamental frequency
    • f1(n=1, 1st harmonic)
  • Nth harmonic frequency
    • fn = n * f1
  • Length of string/pipe
    • L
  • Wave speed
    • v = 340 m/s in pipes

2 models for discussion…

standing waves in strings
Standing Waves in Strings
  • Nodes occur at each end of the string
  • Harmonic # = # of envelopes
  • fn = nv/2L
    • f = frequency
    • n = harmonic #
    • v = wave velocity
    • L = length of string
practice2
Practice
  • An orchestra tunes up by playing an A with fundamental frequency of 440 Hz.
    • What are the second and third harmonics of this note?
  • Solve fn = n*f1
    • f1 = 440
    • f2 = 2 * 440 = 880 Hz
    • f3 = 3 * 440 = 1320 Hz
string practice
String Practice
  • A C note is struck on a guitar string, vibrating with a frequency of 261 Hz, causing the wave to travel down the string with a speed of 400 m/s.
    • What is the length of the guitar string?
  • Solve fn = nv/(2L) for L
    • L = nv/(2f)
    • L = 0.766 m
standing waves in open pipes
Standing Waves in Open Pipes
  • Waves occur with antinodes at each end
  • fn = nv/2L
    • f = frequency
    • n = harmonic #
    • v = wave speed
    • L = length of open pipe
standing waves in pipes closed at one end
Standing Waves in Pipes (closed at one end)
  • Waves occur with a node at the closed end and an antinode at the open end
  • Only odd harmonics occur
  • fn = nv/4L
    • f = frequency
    • n = harmonic #
    • v = wave speed
    • L = length of pipe
pipe practice
Pipe Practice
  • What are the first 3 harmonics in a 2.45 m long pipe that is:
    • Open at both ends
    • Closed at one end
  • Solve
    • (open) fn = nv/(2L) find f1, f2, f3
    • (closed @ 1 end) fn = nv/(4L) find f1, f3, f5
beats
Beats
  • Beats occur when 2 close frequencies (f1, f2) interfere
    • Reinforcementvscancellation
  • Pulsating tone is heard
  • Frequency of this tone is the beat frequency (fb)
  • fb = |f1 - f2|
beats1
Beats

f1

f2

|f1-f2|

Ex. If f1 = 440 Hz and f2 = 420 Hz, then fb = (440-420) = 20 Hz

lab practice
Lab Practice
  • Simulation lab using EXPLORE
    • Standing Waves
    • Wave addition