1. PHYS 218 sec. 517-520 Review Chap. 15 Mechanical Waves

2. What you have to know Defining waves and their properties Wave functions and wave dynamics Energy or power of waves Principle of superposition

3. Types of mechanical waves Mechanical wave: a disturbance that travels through some material (called medium). Transverse wave The displacements of the medium are perpendicular (transverse) to the direction of travel of the wave E.g: wave on a string. In this case the wave travels in the x-direction while the medium (particle of the string) is moving in the y-direction Direction of the travel of the wiggle The point on the string moves vertically. The string itself does NOT move with the wiggle.

4. Longitudinal wave Types of mechanical waves (2) Direction of the travel of the wave The displacements of the medium are back and forth along (longitudinal) the direction of travel of the wave E.g: when the medium is a liquid or gas in a tube As the wave passes, each particle of the fluid moves back and forth parallel to the motion of the wave. But the fluid particles do NOT move away from their original (equilibrium) positions. In addition, there are waves which have both longitudinal and transverse components.

5. Wave speed The speed of the wave propagating through the medium. This is determined by the mechanical properties of the medium. This is NOT the speed of the particle in the medium. Periodic waves When each particle in the medium is in periodic motion Sinusoidal waves Periodic waves when the particles are in Simple Harmonic Motion. Sine or Cosine waves Any periodic waves can be represented as a combination of sinusoidal waves. Wavelength ( ): the length of one complete wave pattern

6. Wave function The function that describes the position (i.e. y-direction) of any particle (i.e., at any x value) at any time (i.e. at any t). Wave function contains all information on the wave.

7. Wave function Particle velocity and acceleration

8. Wave equation

9. Wave speed Wave speed is determined by the properties of the medium. It does not depend on the shape of the wave.

10. In general

11. Ex 15.3Wave speed Speed of the transverse wave If the frequency is 2.0 Hz, how many cycles are there in the rope’s length?

12. Energy in wave motion Waves transport energy power Remember that the particles are moving vertically

13. Wave intensity Intensity (I): average power per unit area Ex 15.3 At a distance of 15 m the intensity of a sound wave is 0.25 W/m 2. At what distance from the siren is the intensity 0.01 W/m 2 ? Unit of power = W Unit of intensity = W/m 2

14. Principle of superposition When two waves meet, the net wave function is the algebraic sum of the two wave functions When two waves meet, they overlap. This overlapping is called interference. If the two waves are in phase, their amplitudes are added and the amplitude of the net wave is larger : constructive interference If the two waves are out of phase, their amplitudes are subtracted and the amplitude of the net wave is smaller : destructive interference

15. Reflection of a wave Fixed end Free end Incident wave Reflected wave

16. Standing wave When a sinusoidal wave is reflected by a fixed end. Incident wave Reflected wave Interference of the two waves This wave does not move. Therefore, STANDING WAVE node antinode Destructive interference Constructive interference Standing wave

17. Normal modes of a string If the string has length L