Waves
Overview
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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
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 – Basic Structure
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
Wave speed is 3 x 108 m/s
Electric & Magnetic fields are perpendicular
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
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
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
2 types of mechanical waves
• Transverse
• “across”
• Longitudinal
• “along”
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
• Particles move parallel to the wave motion,
causing points of compression and rarefaction
• Example - sound
>> Direction of wave motion >>
Longitudinal Waves
Sound
Speed of sound in air depends on temperature
• Ss = 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
Average human ear can detect &
process tones from
• 20 Hz (bass – low frequencies) to
• 20,000 Hz (treble – high frequencies)
Doppler Effect
What is it?
• The apparent change in frequency of sound due
to the motion of the source and/or the observer.
Doppler Effect
Moving car example
Doppler Effect Example
Police radar
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
s
o
vv
vvff'
Sound Barrier #1
Sound Barrier #2
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 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
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 - Superpositionof Waves
Superposition of Waves
Superposition of Waves
Special conditions for amp, freq and λ…
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.
Standing Wave
2 models for discussion…
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
Standing Waves in Strings
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
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 f = nv/(2L) for L
• L = nv/(2f)
• L = 0.766 m
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)
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 #
• L = length of 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)
• (closed @ 1 end) fn = nv/(4L)
Beats
Beats occur when 2 close frequencies (f1, f2) interfere• Reinforcement vs cancellation
Pulsating tone is heard
Frequency of this tone is the beat frequency (fb)
fb = |f1 - f2|
Beats
f1
f2
|f1-f2|