Chapter 14 Vibrations and Waves
14.1- Periodic Motion Periodic motion- motions which repeat in a regular cycle Simple harmonic motion- when the force that restores the object to its equilibrium position is directly proportional to the displacement of the objects
Period (T)- time needed for an object to repeat one complete cycle of motion Amplitude- maximum distance that the object moves from equilibrium
The Mass on a Spring Hooke’s Law- states that the force exerted by a spring is directly proportional to the amount that the spring is stretched (elastic springs only). F=-kx The force exerted by a spring is equal to the spring constant times the distance the spring is compressed or stretched from its equilibrium position.
Potential Energy PE sp =1/2kx 2 k=spring constant x=displacement
How much force is necessary to stretch a spring 0.25 m when the spring constant is 95 N/m? F=-kx
A spring has a spring constant of 256 N/m. How far must it be stretched to give it an elastic potential energy of 48 J? PE sp =1/2kx 2
Page minutes Read 1 st paragraph. Write a 1 sentence summary of the information you have read. Share it with a partner. Discuss any similarities or differences you have written. This will be your exit slip from class today!
Automobiles Bumpers are modified springs to help cars recoil away from the barrier
Pendulums Pendulum- consists of a massive object, called the bob, suspended by a string or light rod of length, l. F T -rod force F g -force of gravity F net - resultant of F g and F T
Period of a Pendulum T=2π√(l/g) The period of a pendulum is equal to two times pi times the square root of the length of the pendulum divided by the acceleration due to gravity.
What is the period on Earth of a pendulum with a length of 1.0 m? T=2π√(l/g)
Resonance Resonance-occurs when small forces are applied at regular intervals to a vibrating or oscillating object and the amplitude of the vibration increases. – Swinging on a swing set – Jumping on a trampoline – Rocking a car to get out of a snow bank – Tacoma Narrows Bridge Collapse Tacoma Narrows Bridge Collapse
TransverseLongitudinal
14.2- Wave Properties Wave-disturbance that carries energy through matter or space Wave Pulse- single bump or disturbance that travels through a medium Periodic Wave- wave moves at the same rate
Mechanical Waves Mechanical Waves- waves that require a medium – Transverse waves- vibrates perpendicular to the direction of the wave’s motion – Longitudinal waves- the disturbance is in the same direction as, or parallel to, the direction of the wave’s motion – Surface waves- has characteristics of both transverse and longitudinal waves
Measuring a Wave Speedv=∆d/∆t Amplitude- maximum distance of the wave from its position of rest, or equilibrium – As energy increases amplitude _______________.
Wavelength- distance from equal points of a wave Trough- low point Crest- high point Compression- most dense area Rarefaction- least dense area
Phase In phase- 2 points equal distances from the equilibrium and the same velocity 180 o out of phase- 2 points with opposite displacements from the equilibrium with equal velocity
Period and Frequency Both only apply to periodic waves not pulses Frequency- the number of complete oscillations it takes each second. Hertz (Hz) f=1/TThe frequency of the wave is equal to the reciprocal of the period
λ=v/f=vTThe wavelength of a wave id equal to the velocity divided by the frequency
A sound wave produced by a clock chime is heard 515 m away 1.50 s later. – What is the speed of the sound of the clock’s chime in air? – The sound wave has a frequency of 436 Hz. What is the period of the wave? – What is the wave’s wavelength?
14.3 Wave Behavior Speed of a wave depends only on the medium it is traveling through
Incident wave- the wave that strikes the boundary of the medium Reflected wave- returning wave Normal- line which is drawn perpendicular to the barrier Law of reflection- the angle of incidence is equal to the angle of reflection
Superposition of Waves Principle of superposition- the displacement of a medium caused by two or more waves is the algebraic sum of the displacements cause by the individual waves
Interference- the result of the superposition of two or more waves – Destructive- equal but opposite wave cancel out and create a node – Constructive- equal and in the same direction wave that combine and create an antinode
Standing wave- the interference of the two traveling waves moving in opposite directions – If the frequency doubles one more node and antinode will appear
Waves in Two Dimensions Wave front- a line that represents the crest of a wave in 2 dimensions and it can be used to show waves of any shape Ray- line drawn at a right angle to the crest of the wave