Vibrations, Waves, & Sound

Chapters 25 & 26

25.1 Vibration of a Pendulum

• When the angle is kept small, the period of the pendulum depends only on its length and the acceleration due to gravity.

• The back-and-forth vibratory motion of a swinging pendulum is called simple harmonic motion.

Period

• The time it takes for one complete cycle of motion.

• Represented by the symbol T• Unit of seconds

Frequency

• The number of cycles completed in a unit of time (usually seconds)

• Represented by the symbol f• Unit of s-1 (also known as Hertz)

Period and Frequency

• Period and frequency are inversely related.

• f = 1/T and T = 1/f

A plucked string vibrates back and forth 10 times each second.

• What is the period?1/10 s

What is the frequency?

10 cycles per second (10 Hz)

25.2 Wave Description

• A wave is an means by which energy is transferred from one place to another via periodic disturbances

• The source of all waves is something that vibrates.

Mechanical Waves• Waves that require a physical medium to travel

through.• Examples of physical media are water, air, string,

slinky.

Electromagnetic waves

• Waves that do not require a physical medium.• Comprised of oscillating electric and magnetic fields• Examples include x-rays, visible light, radio waves,

etc.

25.2 Wave Description

• A sine curve is a pictorial representation of a wave.

Wave Parts• Amplitude - the maximum displacement from

equilibrium.• The high points on a wave are called crests. • The low points on a wave are called troughs.• The wavelength of a wave is the distance from one

part of a wave to the next identical part.

25.5 Transverse Waves• Particles of the medium move perpendicular to the

direction of energy transfer• You should be able to identify crests, troughs,

wavelength (distance traveled during one full cycle), and amplitude

Crest

Trough

25.6 Longitudinal Waves

• Particles of the medium move parallel to the direction of energy transfer

• Be able to Identify compressions, rarefactions, wavelengths

Compressions Rarefactions

25.3 Wave Motion

• When energy is transferred by a wave from a vibrating source to a distant receiver, no matter is transferred between the two points.

Waves transfer energy

• While energy is transferred from point A to point B, the particles in the medium do not move from A to B. – Individual particles of the medium merely vibrate

back and forth in simple harmonic motion

25.4 Wave Speed

• You can calculate the speed of a wave by multiplying the wavelength by the frequency.

Wave speed• Wave speed is determined completely by

the characteristics of the medium– For an unchanging medium, wave speed is

constant

think!If a water wave vibrates up and down two times each second and the distance between wave crests is 1.5 m, what is the frequency of the wave? What is its wavelength? What is its speed?

Answer: The frequency of the wave is 2 Hz; its wavelength is 1.5 m; and its wave speed is 3 m/s.

25.4 Wave Speed

25.7 Interference• The combination of two or more waves in a

medium at the same time.– Matter cannot occupy the same space at the same

time, but energy can.

25.7 Interference

• The Superposition Principle describes what happens when waves interfere…– Waves (energy) pass through each other

completely unaffected– The medium will be displaced an amount equal to

the vector sum of what the waves would have done individually

Constructive Interference-pulses to same side of equilibrium

-resulting medium displacement is greater than original waves

-pulses continue unaffected

Destructive Interference

• Pulses on opposite sides of equilibrium

• Resulting displacement is less than at least one of the originals

• Pulses continue unaffected

Complete Destructive Interference

Interference patterns

• Out of phase – destructive interference

• In phase – constructive interference

25.8 Standing Waves

• A wave pattern that results when two waves of the same frequency, wavelength, and amplitude travel in opposite directions and interfere.

25.8 Standing Waves

• Only certain frequencies produce standing wave patterns.

25.8 Standing Waves•Nodes are areas of complete destructive interference and have no displacement•Antinodes are areas of constructive interference and have maxiumum displacement

25.9 The Doppler Effect• As a wave source approaches, an observer

encounters waves with a higher frequency. As the wave source moves away, an observer encounters waves with a lower frequency.

25.9 The Doppler Effect

• The greater the speed of the source, the greater will be the Doppler effect.

• Family Video

25.9 The Doppler Effect

• The Doppler effect also occurs for light.• When a light source approaches, there is an

increase in its measured frequency (blue shift)• When it recedes, there is a decrease in its

frequency (red shift)

26.1 The Origin of Sound

• All sounds originate in the vibrations of material objects.

• Pitch is the human perception of frequency

26.1 The Origin of Sound

• The normal range of human hearing is 20 to 20,000 hertz.

• Sound waves with frequencies below 20 hertz are called infrasonic.

• Sound waves with frequencies above 20,000 hertz are called ultrasonic.

26.2 Sound in Air

• Consider sound waves in a tube.• When the prong of a tuning fork next to the tube

moves toward the tube, a compression enters the tube.

• When the prong swings away, in the opposite direction, a rarefaction follows the compression.

• As the source vibrates, a series of compressions and rarefactions is produced.

26.3 Media That Transmit Sound

• The speed of sound differs in different materials.

• In general, sound is transmitted faster in liquids than in gases, and still faster in solids.

• Sound cannot travel in a vacuum.• Bell in vacuum

26.4 Speed of Sound

• The speed of sound depends on the characteristics of the medium. A material’s temperature, mass of particles, density, and elasticity are all factors. – Helium & Sulfur Hexafluoride

- In room temperature air, sound travels about 340 m/s- In water, sound travels about 1200 m/s- In aluminum, sound travels about 5000 m/s

26.6 Natural Frequency

• When any object composed of an elastic material is disturbed, it vibrates at its own special set of frequencies, which together form its special sound.

26.7 Forced Vibration

• Sounding boards are an important part of all stringed musical instruments because they are forced into vibration and produce the sound.

26.8 Resonance

• If the frequency of a forced vibration matches an object’s natural frequency, resonance dramatically increases the amplitude.

• Resonance occurs whenever successive impulses are applied to a vibrating object in rhythm with its natural frequency.

Resonance Videos

• How to Break a Glass• Jaime Vendera• Tacoma Narrows Bridge

Reflection

• The bouncing of a wave when it encounters the boundary between two different media

Fixed End Reflection

• At a fixed boundary, waves are inverted as they are reflected.

Free End Reflection

• At a free boundary, waves are reflected on the same side of equilibrium