Waves
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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 basic structure

Wave – Basic Structure


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 >>


Longitudinal waves

Longitudinal Waves


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 example

Doppler Effect Example

  • Police radar


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 1

Sound Barrier #1


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 waves

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.


Standing wave1

Standing Wave


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


Standing waves in strings1

Standing Waves in Strings


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


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