1. PHY238Y Lecture 5 Waves (general discussion) Transverse and longitudinal waves 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., Wiley 2003, Ch. 17 (17.4 – 17.8) Thanks to dr. R. Nave for the permission to use some of the pictures from Hyper Physics : http://hyperphysics.phy-astr.gsu.edu http://hyperphysics.phy-astr.gsu.edu

2. PHY238Y Lecture 5 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 x 1 + x 2 = A cos  p t x 1 - x 2 = B cos  s t where and

3. PHY238Y Lecture 5 Going from oscillators to waves:

4. PHY238Y Lecture 5 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

5. PHY238Y Lecture 5 Transverse waves: displacement is perpendicular to the direction of travel Longitudinal waves: displacement is in the same direction as the direction of travel

6. PHY238Y Lecture 5 Wavelength and frequency: Periodic motion: PeriodPeriod: the time required to complete a full cycle, T in seconds/cycle FrequencyFrequency: the number of cycles per second, f in 1/seconds or Hertz (Hz) Amplitude: the maximum displacement from equilibrium Amplitude For a traveling wave, one needs also: Velocity of propagation: v Velocity of propagation Wavelength: repeat distance of wave Wavelength

7. PHY238Y Lecture 5 Transverse Traveling Wave Parameters

8. PHY238Y Lecture 5 Equivalent forms of wave solution: The speed of a traveling wave v is defined by:

9. PHY238Y Lecture 5 Wave speed in a stretched string : a pulse propagating along a string causes additional stretching

10. PHY238Y Lecture 5 The speed of a wave in a stretched string is a function of the elastic properties of the medium 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