Mechanical Waves Introduction to Waves Types of Waves Traveling - - PDF document

Mechanical Waves

• Introduction to Waves
• Types of Waves
• Traveling Waves
• Waves on a String
• Homework

1

Introduction to Waves

• Wave motion appears in almost every branch
• f physics, e.g. sound, light, radio and other

electromagnetic waves

• A wave is a disturbance that travels at a def-

inite speed (v=λf) and transfers energy and momentum

• Mechanical waves travel in elastic media (e.g.

sound)

• Electromagnetic waves are oscillating elec-

tromagnetic fields and do not require a medium (the speed of EM waves in a vacuum is c=3x108 m/s)

2

Types of Waves

• Transverse waves - displacement is perpen-

dicular to direction of propagation

– Traveling wave on a string

• Longitudinal wave - displacement is parallel

to direction of propagation

– Traveling wave in a spring Sound 3

Transverse Waves

• Displacement is perpendicular to direction
• f propagation

– Traveling wave on a string 4

Longitudinal Waves

• Displacement is parallel to direction of prop-

agation

– Traveling wave in a spring – Sound 5

Traveling Waves

• The wavefunction for a wave traveling in the

+x direction has the form y(x, t) = f(x − vt)

• The wavefunction for a wave traveling in the
• x direction has the form

y(x, t) = f(x + vt)

6

Sinusoidal Waves y(x, t) = A sin

    

2π λ (x − vt)

    

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Sinusoidal Waves (cont’d)

• Wavelength (λ) is the distance between two

adjacent points in the wave having the same phase

• The period (T) is the time required for the

wave to travel one wavelength, λ = vT y(x, t) = A sin

   2π    x

λ − t T

       

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Sinusoidal Waves (Cont’d) y(x, t) = y(x + λ, t) = y(x + 2λ, t) = . . . y(x, t) = y(x, t + T) = y(x, t + 2T) = . . .

• The wavefunction can also be written as

y = A sin (kx − ωt) where k = 2π

λ is the wave number and ω = 2π T = 2πf is the angular frequency

• The speed of the wave is

v = λ T = ω k = λf

• If y = 0 at x = 0 and t = 0

y = A sin (kx − ωt + φ) where φ is the phase constant

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Speed of Waves on a String Fr = 2T sin θ ≃ 2Tθ m = µ∆s = 2µRθ Fr = mv2 R 2Tθ = 2µRθv2 R v =

• T

µ

10

Homework Set 24 - Due Wed. Nov. 10

• Read Sections 13.1-13.4
• Answer Questions 13.2, 13.9, 13.10 & 13.11
• Do Problems 13.1, 13.2, 13.3, 13.5, 13.10,

13.13 & 13.14

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