Physics 101: Lecture 20 Waves Final Physics 101: Lecture 20 Waves 1

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

Period and Velocity 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: The distance  between identical points on the wave. Amplitude: The maximum displacement A of a point on the wave. Angular Frequency w: w = 2 p f Wave Number k: k = 2 p / l Recall: f = v / l Add stuff here  Wavelength y Amplitude A A x 20

Example: microwave 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 = 3x108 m/s 29

Interference and Superposition When too waves overlap, the amplitudes add. Constructive: increases amplitude l2-l1 = m λ Destructive: decreases amplitude l2-l1 = (m+1/2) λ Do this with springs 34

Example: two speakers 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 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 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) Inverted B) Upright Fixed boundary reflected wave inverted Free boundary reflected wave upright Use large spring as demo here 37

Standing Waves Fixed Endpoints Fundamental n=1 ln = 2L/n fn = n v / (2L) Two people with large spring, can produce all of these as demo. 44

Velocity of Waves on a string µ = mass per unit length of string As µ increases, v increases, f decreases (λ fixed) Long Spring and slinky equal length (8 feet each) speeds up a LOT in slinky because mu is small and T is same. 17

Example: guitar 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 329.63 Hz, what is the mass of the string? Calculate tension in guitar string given mass density and frequency. Ch 11 # 45 48

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