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|