CP Physics Chapter 12CP Physics Chapter 12

WavesWaves

Hooke’s LawHooke’s LawFspring = kx

During the periodic motion

•At equilibrium, velocity reaches a maximum (b)

•At maximum displacement, spring force and acceleration reach a maximum (a & c)

•A stretched or compressed spring has elastic potential energy.

ExamplesExamples

1. A load of 45 N attached to a spring that is hanging vertically stretches the spring 0.14 m. What is the spring constant?

2. If a mass of 0.55 kg attached to a vertical spring stretches the spring 36 cm from its equilibrium position, what is the spring constant?

Measuring SHMMeasuring SHM Amplitude (A)Amplitude (A) – the maximum – the maximum

displacement from equilibrium.displacement from equilibrium.

Period (T)Period (T) –time it takes to complete one –time it takes to complete one cycle, SI unit is secondscycle, SI unit is seconds

Frequency (f)Frequency (f) –how many complete cycles –how many complete cycles of motion in a unit of time, SI unit is hertz of motion in a unit of time, SI unit is hertz (Hz)(Hz)

f = 1/Tf = 1/T

Simple Harmonic MotionSimple Harmonic Motion

Spring/mass Simple Pendulum

T 2m

k

T 2L

g

ExamplesExamples

3. You are designing a pendulum clock to have a period of 1.0 s. How long should the pendulum be?

4. A mass of 0.30 kg is attached to a spring and is set into vibration with a period of 0.24 s. What is the spring constant of the spring?

Example #5Example #5

A 0.75 kg mass attached to a vertical spring A 0.75 kg mass attached to a vertical spring stretches the spring 0.30 m.stretches the spring 0.30 m.

A.A. What is the spring constant?What is the spring constant?

B.B. The mass-spring system is now placed on The mass-spring system is now placed on a horizontal surface and set vibrating. a horizontal surface and set vibrating. What is the period of the vibration?What is the period of the vibration?

Example #6Example #6

Calculate the period and frequency of a 3.500 Calculate the period and frequency of a 3.500 m long pendulum at the following locations:m long pendulum at the following locations:

A) The North Pole, where g = 9.832 m/s2A) The North Pole, where g = 9.832 m/s2

B) Chicago, where g = 9.803 m/s2B) Chicago, where g = 9.803 m/s2

C) Jakarta, Indonesia, where g = 9.782 m/s2C) Jakarta, Indonesia, where g = 9.782 m/s2

SHM and WavesSHM and Waves

Wave PartsWave Parts AmplitudeAmplitude Time periodTime period Wavelength – distance Wavelength – distance

from same point to same from same point to same point (i.e. peak to peak)point (i.e. peak to peak)

Crest – “peak”Crest – “peak” Trough – “valley”Trough – “valley”

f

TTv

1

Wave TypesWave Types

Pulse WavePulse Wave: A single, non-periodic : A single, non-periodic disturbance. If you hold a rope attached to disturbance. If you hold a rope attached to a wall, you create a pulse wave if you give a wall, you create a pulse wave if you give a single flip of your wrist.a single flip of your wrist.

Periodic WavePeriodic Wave: A wave whose source is : A wave whose source is some form of periodic motion. If you move some form of periodic motion. If you move your hand up & down repeatedly, you your hand up & down repeatedly, you produce a periodic waveproduce a periodic wave

Wave TypesWave Types

Transverse WaveTransverse Wave: A wave whose : A wave whose particles vibrate perpendicularly to the particles vibrate perpendicularly to the direction of wave motion.direction of wave motion.

Wave TypesWave Types Longitudinal Wave: A wave whose particles Longitudinal Wave: A wave whose particles

vibrate parallel to the direction of wave motion.vibrate parallel to the direction of wave motion.

This type of wave is also called a density or This type of wave is also called a density or pressure wave. The crest areas are areas of pressure wave. The crest areas are areas of high density or pressure called high density or pressure called compressions.compressions. The troughs are areas of low density or pressure The troughs are areas of low density or pressure called called rarefactions.rarefactions.

Important Truth About ALL WavesImportant Truth About ALL Waves

Waves transfer ENERGY. Waves transfer Waves transfer ENERGY. Waves transfer energy by transferring motion, NOT by energy by transferring motion, NOT by transferring matter. The rate at which a transferring matter. The rate at which a wave transfers energy depends on the wave transfers energy depends on the AMPLITUDE at which the particles of the AMPLITUDE at which the particles of the medium vibrate.medium vibrate.

Example #7Example #7

A piano emits frequencies that range from a low of about 28 Hz to a high of about 4200 Hz. Find the range of wavelengths in air attained by this instrument when the speed of sound in air is 340 m/s.

Example #8Example #8

The red light emitted by a He-Ne laser has The red light emitted by a He-Ne laser has a wavelength of 633 nm in air and travels a wavelength of 633 nm in air and travels at 3.00 x 108 m/s. Find the frequency of at 3.00 x 108 m/s. Find the frequency of the laser light.the laser light.

InterferenceInterference

Constructive Interference

Individual displacements on the same side of

equilibrium are added together to form the

resultant wave.

InterferenceInterference

Destructive Interference

Individual displacements on opposite sides of

equilibrium are added together to form the

resultant wave.

Properties of WavesProperties of WavesReflectionReflection

Standing WavesStanding Waves A standing wave is the wave pattern that results A standing wave is the wave pattern that results

when two waves of the same frequency, when two waves of the same frequency, wavelength & amplitude travel in opposite wavelength & amplitude travel in opposite directions and interfere.directions and interfere.

Standing waves have nodes & antinodes.Standing waves have nodes & antinodes. NodeNode: undergoes total destructive interference & is : undergoes total destructive interference & is

therefore stationary.therefore stationary. AntinodesAntinodes: Half way between two nodes. Total : Half way between two nodes. Total

constructive interference and therefore the point of the constructive interference and therefore the point of the largest amplitude.largest amplitude.

Standing WavesStanding Waves

Example #9Example #9

A wave of amplitude 0.30 m interferes with a A wave of amplitude 0.30 m interferes with a second wave of amplitude 0.20 m. What is second wave of amplitude 0.20 m. What is the largest resultant displacement that may the largest resultant displacement that may occur?occur?

Example #10Example #10

A string is rigidly attached to a post at one A string is rigidly attached to a post at one end. Several pulses of amplitude 0.15 m end. Several pulses of amplitude 0.15 m sent down the string are reflected at the post sent down the string are reflected at the post and travel back down the string without a and travel back down the string without a loss of amplitude. What is the amplitude at loss of amplitude. What is the amplitude at a point on the string where the maximum a point on the string where the maximum displacement points of two pulses cross? displacement points of two pulses cross? What type of interference is this?What type of interference is this?

Example #11Example #11

How would your answer to problem 2 How would your answer to problem 2 change if the same pulses were sent down a change if the same pulses were sent down a string whose end is free? What type of string whose end is free? What type of interference is this?interference is this?