Waves Waves

Types of Waves l Longitudinal: The medium oscillates in the same direction as the wave is moving è Sound l Transverse: The medium oscillates perpendicular to the direction the wave is moving. è Water (more or less) è The “Wave” 8

Period and Velocity l Period: The time T for a point on the wave to undergo one complete oscillation. Speed: The wave moves one wavelength in one period T so its speed is v =  / T. 22

Slinky Question Suppose that a longitudinal wave moves along a Slinky at a speed of 5 m/s. Does one coil of the slinky move through a distance of five meters in one second? 1. Yes 2. No 5m 12

Harmonic Waves Wavelength Wavelength: The distance between identical points on the wave. Amplitude: The maximum displacement A of a point on the wave. Amplitude A A 20 Angular Frequency  :  = 2  f x y Wave Number k: k = 2  / Recall: f = v /

l The wavelength of microwaves generated by a microwave oven is about 3 cm. At what frequency do these waves cause the water molecules in your burrito to vibrate ? The speed of light is c = 3x10 8 m/s Example: microwave 29

Interference and Superposition l When too waves overlap, the amplitudes add. è Constructive: increases amplitude l 2 -l 1 = m λ è Destructive: decreases amplitude l 2 -l 1 = (m+1/2) λ 34

Example: two speakers l Two speakers are separated by a distance of 5m and are producing a monotone sound with a wavelength of 3m. Other than in the middle, where can you stand between the speakers and hear constructive interference?

Example: two speakers l Two speakers are separated by a distance of 5m and are producing a monotone sound with a wavelength of 3m. Where can you stand between the speakers and hear destructive interference?

Reflection Act l A slinky is connected to a wall at one end. A pulse travels to the right, hits the wall and is reflected back to the left. The reflected wave is A) InvertedB) Upright è Fixed boundary reflected wave inverted è Free boundary reflected wave upright 37

Standing Waves Fixed Endpoints l Fundamental n=1 n = 2L/n l f n = n v / (2L) 44

Velocity of Waves on a string 17 µ = mass per unit length of string As µ increases, v decreases, f decreases ( λ fixed)

Example: guitar 48 A guitar’s E-string has a length of 65 cm and is stretched to a tension of 82N. If it vibrates with a fundamental frequency of Hz, what is the mass of the string?

Summary l Wave Types è Transverse (eg pulse on string, water) è Longitudinal (sound, slinky) l Harmonic  y(x,t) = A cos(  t –kx) or A sin(  t – kx) l Superposition è Just add amplitudes l Reflection (fixed point inverts wave) l Standing Waves (fixed ends)  n = 2L/n è f n = n v / 2L 50