1 PHY238Y Lecture 5-6 n Waves (general discussion) n Transverse and longitudinal waves n Properties of waves: - Amplitude and phase - Wavelength and angular number - Period, angular frequency, frequency § Transverse waves on strings: speed of a traveling wave on a stretched string References: Haliday, Resnick , Walker: Fundamentals of Physics, 6 th ed., Ch. 17 (17.1 – 17.8) or: 7th ed. Ch. 16 (16.1 - 16.8) Thanks to dr. R. Nave for the permission to use some of the pictures from Hyper Physics: http://hyperphysics.phy -astr.gsu.edu PHY238Y Lecture 5 n What we did last time: - Analyzed a system of coupled oscillators; - Found the normal modes, - Found the general solution as a superposition of normal modes q1 q2 mg mg mg mg x 1 + x 2 = A cos w p t x 1 -x 2 = B cos w s t where L g p = ϖ and m k 2 L g s = ϖ t cos 2 B t cos 2 A ) t ( x t cos 2 B t cos 2 A ) t ( x s p 2 s p 1 ϖ ϖ ϖ ϖ - = + =
Transcript
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PHY238YLecture 5-6
n Waves (general discussion)n Transverse and longitudinal wavesn Properties of waves:- Amplitude and phase- Wavelength and angular number- Period, angular frequency, frequency§ Transverse waves on strings: speed of a traveling wave on a
stretched string
References: Haliday, Resnick , Walker: Fundamentals of Physics, 6th
ed., Ch. 17 (17.1 – 17.8) or: 7th ed. Ch. 16 (16.1 - 16.8) Thanks to dr. R. Nave for the permission to use some of the pictures from Hyper Physics:
http://hyperphysics.phy-astr.gsu.edu
PHY238YLecture 5
n What we did last time:- Analyzed a system of coupled
oscillators;
- Found the normal modes,
- Found the general solution as a superposition of normal modes
θ1 θ2
mg mg
mg mg
x1 + x2 = A cosω ptx1 - x2 = B cosωstwhere
Lg
p =ω andmk2
Lg
s +=ω
tcos2B
tcos2A
)t(x
tcos2B
tcos2A
)t(x
sp2
sp1
ωω
ωω
−=
+=
2
PHY238YLecture 5
n Going from oscillators to waves:
mg mg
∆x x ∆x
xn-1 xn xn+1
PHY238YLecture 5
n Fundamental concepts in classical Physics: particle and wave
localized mass, carries energy
fills all the space, energy is distributed
§ Three types of waves:
§ mechanical § electromagnetic § matter waves
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PHY238YLecture 5
n Transverse waves: displacement is perpendicular to the direction of travel
n Longitudinal waves: displacement is in the same direction as the direction of travel
PHY238YLecture 5
n Wavelength and frequency:
Periodic motion:Period: the time required to
complete a full cycle, T in seconds/cycle
Frequency: the number of cycles per second, f in 1/seconds or Hertz (Hz)
Amplitude: the maximum displacement from equilibrium A
For a traveling wave, oneneeds also:n Velocity of propagation: vn Wavelength: repeat
distance of wave
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PHY238YLecture 5
n TransverseTraveling WaveParameters
PHY238YLecture 5
n Equivalent forms of wave solution:
n The speed of a traveling wave v is defined by:
λλ
π
λπ
ω
fvspeedwaveTtx
Atxy
vtxAtxy
tkxAtxy
=
−=
−=
−=
:
2sin),(
)(2
sin),(
)sin(),(
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PHY238YLecture 5
n Wave speed in a stretched string: a pulse propagating along a string causes additional stretching
PHY238YLecture 5
n The speed of a wave in a stretched string is a function of the elastic properties of the medium
n The wavelength of a wave is determined by:
- frequency, fixed by whatever generates the wave;
- wave speed, determined by the internal elastic properties of the medium
