Speed of Waves Speed of waves in strings (review): Speed of longitudinal waves in a solid rod: E - Young’s modulus - density m - mass V - volume F - tension - linear density m - mass L – length of the string The Young’s modulus is the stress divided by the strain. Young’s modulus (optional): Stress: Strain: 1

Speed of sound waves in an ideal gas: - ratio of heat capacities T - temperature in Kelvin t - temperature in Celsius M - molar mass R - gas constant R= J/mol K Speed of sound waves in a fluid: B - bulk modulus - density V - volume P - pressure Speed of Waves (continued) For air: 2

Speed of Sound in Some Common Substances 1. Air (20 o C) 344 Substance Speed (m/s) 3. Water (0 o C) 1, Human tissue 1, Aluminum 6, Iron and steel 5, Lead 1, Helium (20 o C) 999 3

Reflection in out normal to surface b) Diffuse reflection a) Mirror reflection c) Reflection from curved surfaces acoustical mirrors (curved mirrors) whispering galleries S S’S’ sourceimage wall (mirror) 4

Refraction: Snell’s Law index of refraction: Example: n1n1 n2n2 n3n3 In optics: Sound waves in atmosphere when temperature varies with height Sound traveling against the wind Mirage 5

Doppler Effect What do you hear when a sound-emitting object (train, car) passes you? The sound changes in pitch (frequency) as the object goes. Why does this happen? Because the speed of a wave in a medium is constant, change in will affect change in f. v L or v S is “+” if in the same direction as from listener to source and is “-” otherwise Velocity of listener (L): v L Velocity of source (S): v S Velocity of sound: v As the object travels towards you, the distance between wavefronts is compressed; this makes it seem like is smaller and frequency is higher. As the object travels away from you, the distance between wavefronts is extended; this makes it seem like is larger and frequency is lower. 6

The waves spread out from the opening! Diffraction 1) What it is? The bending of waves behind obstacles or apertures into the ”shadow region”, that can be considered as interference of many waves. 2) Haw to observe? Diffraction is most pronounced when the wavelength of the wave is similar to the size of the obstacle or aperture. For example, the diffraction of sound waves is commonly observed because the wavelength of sound is similar to the size of doors, etc. Waves will diffract around a single slit or obstacle. The resulting pattern of light and dark stripes on a screen is called a diffraction pattern (fringes). This pattern arises because different points along a slit create wavelets that interfere with each other just as a double slit would. 7

Example: In order to obtain a good single slit diffraction pattern, the slit width could be: A. /100; B. /10; C. ; D. 10 ; E.100 3a) Diffraction from a single slit (intensity) Minima (dark fringes): 8

Example: Light of wavelength 610 nm is incident on a slit 0.20 mm wide and the diffraction pattern is produced on a screen that is 1.5 m from the slit. What is the width of the central maximum? Example: Light of wavelength 687 nm is incident on a single slit 0.75 mm wide. At what distance from the slit should a screen be placed if the second dark fringe in the diffraction pattern is to be 1.7 mm from the center of the screen? 9