General Physics 2 Induction 1

Introduction to Waves

• A wave is a disturbance that moves through a medium while the medium remains essentially at rest

• Examples• Water, sound, tension, seismic

General Physics 2 Waves & Sound 2

Wave Motion

General Physics 2 Waves & Sound 3

Wave Motion

General Physics 2 Induction 4

Sinusoidal Wave

• One-dimensional waves

• Symbols• A amplitude, k wavenumber, λ wavelength, ω angular

frequency, T period, f frequency

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f x, t( ) = Asin kx −ωt( )

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k ≡2π

λ

€

ω ≡2π

T

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f ≡ω

2π=1

T

General Physics 2 Waves & Sound 5

Wave Characteristics

General Physics 2 Waves & Sound 6

Velocity of Waves

• For all waves:

• For a wave on a string or cord (string instruments):

where:• FT = tension in string• m = mass of string• L = length of string • m/L may also be written as

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=ωk=λ

T

General Physics 2 Induction 7

Wave Equation

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0 = b∂ 2 f

∂t 2−∂ 2 f

∂x 2

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v =1

b

Solution to the wave equation

• Plugging into the wave equation,

General Physics 2 Induction 8

€

f x, t( ) = Asin kx −ωt( )

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df x, t( )dt

= −ωAcos kx −ωt( )

d2 f x, t( )dt 2

=ω2Asin kx −ωt( )

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df x, t( )dx

= kAcos kx −ωt( )

d2 f x, t( )dt 2

= −k 2Asin kx −ωt( )

€

0 = b∂ 2 f

∂t 2−∂ 2 f

∂x 2

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0 =ω2Asin kx −ωt( ) − (−)k 2Asin kx −ωt( )

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b =ω2

k 2= v 2

General Physics2 Simple Harmonic Motion 9

Graphs• The graphs show:

• (a) displacement as a function of time

• (b) velocity as a function of time

• (c ) acceleration as a function of time

• velocity is 90o out of phase with the displacement

• acceleration is 180o out of phase with the displacement

General Physics 2 Waves & Sound 10

Plug & Chug

General Physics 2 Waves & Sound 11

Types of waves

• Transverse• displacement is

perpendicular to velocity• Ex - light

• Longitudinal• displacement is parallel

to velocity• Ex - sound

General Physics 2 Induction 12

Group Problems

(a) AM radio signals have frequencies between 550 kHz and 1600 kHz and travel with a speed of 3.00 x 108 m/s. What are the wavelengths of these signals?

(b) On FM, the frequencies range from 88.0 MHz to 108 MHz and travel at the same speed. What are their wavelengths?

• E15B.1, E15B.7, E15S.1