Chapter 14 Vibrations and Waves. 14.1- Periodic Motion Periodic motion- motions which repeat in a regular cycle Simple harmonic motion- when the force.

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

• PEsp=1/2kx2

• 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?

• PEsp=1/2kx2

Page 378- 5 minutes

• Read 1st 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.

• FT-rod force

• Fg-force of gravity

• Fnet- resultant of Fg and FT

• 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

Transverse Longitudinal

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

• Speed v=∆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

• 180o 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=vT The 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