#### Transcript Waves - ksmithscience

Waves Hooke’s Law Robert Hooke 1678 Felastic = k x Felastic – elastic force (Newtons) k – spring constant (N/m) x – displacement (meters) Spring Constant • Measures the stiffness of the spring • The greater the value of the k means a stiffer spring because a greater force is needed to stretch or compress that spring Hooke’s Law ex: Fel = k x k=F/x #1 k = 1N / 1 cm K = 1 N /cm #2 k = 2 N/2 cm K = 1 N/cm #1 #2 Plot Hooke’s Law from the previous information. What is the spring constant? Spring Constants • More information • Hooke’s Law Problems - homework Simple Harmonic Motion A vibration about an equilibrium position (in which a restoring force is proportional to displacement from equilibrium) F and a max F and a max v max The motion of Earth orbiting the sun is periodic. Is this motion simple harmonic? Why or why not? No; because Earth does not oscillate about an equilibrium position What is equilibrium, amplitude, period and frequency? Amplitude The maximum displacement from equilibrium Period The time that it takes a complete cycle to occur Measured in seconds T = 1 / f frequency The number of cycles or vibrations per unit of time Measured in Hertz ( Hz)= 1 / s f = 1 / T What is equilibrium, amplitude, period and frequency? What is the equilibrium of the spring? Period of a Pendulum or spring Pendulum L = length(m) Spring M= mass (kg) T = 2p L/ g g= gravity( 10 m/s2) T =2p m /k k = spring constant(N/m) Pendulum Ex: You need to know the height of a tower, but darkness obscures the ceiling. You note that a pendulum extending from the ceiling almost touches the floor and that its period is 12 s. How tall is the tower? What is the frequency of the pendulum? T = 2p L/ g (T) 2 = (2 p L / g)2 T 2 = 4 p2 L / g L= gT 2 = 10 m/s2(12s)2 4 p2 4 p2 L = 37 m f = 1 / T = 1/ 12 = 0.08 Hz Spring Ex: A 5 N weight oscillates on a spring that has a displacement of 45 cm. What is the period of the spring? What is the frequency? k = f / x = 5 N / 0.45 m = 11 N / m T = 2p m/k = 2p .5kg/ 11N/m = 1.3 s f = 1 / T = 1 / 1.3 s = 0.77 Hz Pendulum and Spring Problems Types of Waves 1. Mechanical – a wave that propogates through a deformable elastic medium (needs a medium to travel) 2. Electromagnetic – do not a medium to travel Mechanical Waves Longitudinal waves - Waves move parallel to the wave direction EX: Sound Wave Electromagnetic Wave Transverse wave - Waves move perpendicular to the wave direction EX: Light Wave Pulse Wave Throwing a stone in a pond would be a pulse Speed of a Wave Speed of a mechanical wave is constant for any given medium Temperature determines speed V = f l V = velocity (m/s) F = frequency ( Hz) l= wavlength ( m) Wave Speed EX: A piano string tuned to middle C vibrates with a frequency of 262 Hz. Assuming the speed of sound is 343 m/s, find the wavelength of the sound waves produced by the string. V = f l f=v / l f = 343 m/s = 1.31 262 Hz Waves Anatomy Go to the following website to answer the questions. • Transverse Waves 1. Define a transverse wave 2. Draw and label the parts of a transverse wave 3. Define the parts Waves Anatomy Go to the following website to answer the questions. • Longitudinal Wave 1. Define a longitudinal wave 2. Draw and label the parts of a longitudinal wave 3. Define the parts Standing Wave Draw a standing wave labeling the nodes and antinodes • Make your own standing waves Harmonics Draw a 1st, 2nd and 3rd Harmonic Reflection- Study the animations to determine the difference between a fixed and free reflection • Fixed • Free Interference • 1. Define Constructive and Destructive Interference • 2. Adjust the points make a crest and trough, on the left and right. Hit the run button and see what happens. • http://id.mind.net/~zona/mstm/physics/wav es/interference/intrfrnc.html