Unit Three: Waves and SoundChapter Six, Seven and Eight

6.1 VibrationsWaves transfer energy over a distance in the form of a disturbance. This disturbance can be caused by the vibration of an object. A vibrating object has a ‘rest’ position and will periodically shift from this state to another. Think of the type of vibrational motion exhibited in the following examples.

A weight hanging from a spring.A weight hanging from a rope and the rope is twisted. A pendulum. A piece of wood floating in the ocean.

Periodic motion occurs when an object repeats a pattern of motion. The vibration, or oscillation is repeated over and over with the same time interval.

Types of Vibrations There are 3 basic types of vibrations: transverse vibrations, longitudinal vibrations, and torsional vibrations. A transverse vibration occurs when an object vibrates perpendicular to its axis at the normal rest position (such a pendulum).A longitudinal vibration occurs when an object travels parallel to its axis at the rest position.

axis

movement

axis

movement

A torsional vibration occurs when an object twists around its axis at the rest position, for example a human twisting to the left or the right periodically.

Observe the twist to the left, then the rest position, then the twist to the right.

One complete oscillation of a vibrating object is called a cycle. A cycle would be complete relative to a point in the object’s vibration. This is when the object travels past that point in the same direction.

Possible cycles:

1,2,3,2,1 or 2,3,2,1,2 or

3,2,1,2,3 Not 2,3,2 !!!

The number of cycles which occur per second is called the frequency of vibration (f). Frequency is measured in hertz (Hz) or s-1. The period of vibration (T) is the time required to complete one cycle. Period is measured in seconds.

fT

T

cyclef

cycles

tT

t

cyclesf

11

#

#

The distance in either direction from the equilibrium, or rest position to maximum displacement is called the amplitude (A) of vibration.

Objects that are ‘in phase’ vibrate with the same period and pass through the rest position at the same time and in the same direction.

In phase In phase Out of phase

p. 198 1-8 p.202 1-11 Inertial Balance Activity

Inertial Balance Activity

Inertial balances are useful for measuring the mass of items when the force of gravity is not present or strong enough to do so.

Inertial balances vibrate back in force after being set in motion. If the amplitude is not large then the period of vibration is constant even while the amplitude diminishes.

Obtain 8 sets of data using the inertial balance. Record the mass of plates, washers, nut and bolt. Record the number of oscillations (at least 10) and the time of oscillations.

Prepare a observations results table with the following headings: mass, # oscillations, time, period, period2, frequency (include units).

Make a graph of mass (y) vs. period2 (s). Draw in a line of best fit and calculate the equation of the line.

224

2 Tk

mork

mT

6.2 Wave Motion

Waves transfer energy over a distance in the form of a disturbance. In transverse waves, particles in the medium move at right angles to the direction in which the wave travels. The high section of the wave is called the crest and the low section is a trough. The rest position is known as equilibrium. A wave that consists of a single disturbance is a pulse (may be positive or negative). Periodic waves originate from periodic vibrations where the motions are continuous and repeated in the same time intervals.

Wavelength (λ)

Crest

Trough

AmplitudeWavelength (λ)

As the wave travels through any medium, its amplitude will decrease due to energy loss from friction. If no energy were required to overcome friction, an ‘ideal wave’ would be present.

Longitudinal wavesIn longitudinal waves, particles vibrate parallel to the direction of motion of the wave. The most common longitudinal waves are sound waves. In a longitudinal wave, regions where the particles are closer together than normal are known as compressions and the regions where they are farther apart than normal are known as rarefactions.

v

Compression Rarefaction RarefactionCompression

Wavelength (λ)

Wavelength (λ)

The amplitude will be the change in a physical quantity from the rest position to a maximum compression or minimum rarefaction. For sound this quantity would be air pressure.

Homework: p.208 3,4

Demonstrate pulses, waves, reflections, reflection transmission, speed of medium then change, superposition. Phet.

6.3 The Universal Wave Equation

A wave travels one wavelength in one period of time.

fvT

fbutT

v

t

dv

1

f = frequency

= wavelength

The speed of a wave is a property of the medium it travels in.

The distance between successive crests in a series of water waves is 4.0m. The crests travel 9.0m in 4.5s. What is the frequency of the crests?

Δd = 9.0m

Δt = 4.5s

λ = 4.0m

f = ? Hzf

f

ft

d

5.0

)4(5.4

9

Homework: p.211 1,2 p, 211 1-8 (hand in)

6.4 Transmission and Reflections of Waves Waves behave in various ways A change in the medium in which a wave is traveling often results in a change of the speed of the wave. The frequency of the wave or disturbance will never change however the wavelength of the wave must change if the Universal Wave Equation is to be upheld. Changes to the speed of the wave will ensure proportional changes in the wavelength of the wave.

When waves undergo fixed end reflection the pulse is inverted. If the reflection occurs from a free end then there is no inversion. In both fixed end and free end reflection there is no change in frequency or wavelength. There is also no change in the speed of the pulse since the medium is the same.

Fixed end

Free end

Inverted reflected pulse

Reflected wave is not inverted

When a wave travels into a new medium partial reflection occurs. Some of the energy of the wave is transferred through to the new medium, but some is also reflected back into the original medium. Of course, since the wave is traveling into a new medium there will be a change in its wavelength and speed. The loss of energy also means a decrease in amplitude for the wave.

Fast to Slow Medium (Less dense to more dense Medium)The slow medium acts like a rigid obstacle, and the reflected wave is inverted. The transmitted wave is not inverted, travels with reduced speed and wavelength and has a diminished amplitude.

Slow to Fast Medium (More dense to less dense Medium)The fast medium acts like a free end and the reflected wave is not inverted. The transmitted wave is not inverted, travels with increased speed and wavelength and has a diminished amplitude.

Incident Pulse

Fast Medium

Reflected pulse

Slow Medium

Transmitted Pulse

Incident Pulse

Fast Medium

Transmitted pulse

6.6 Interference of Waves

Wave interference occurs when two waves act simultaneously on the particles of a medium. There are two types of interference: constructive and destructive.

Destructive interference occurs when a crest meets a trough. Constructive interference occurs when crests meet crests (supercrests) or troughs meet troughs (supertroughs).

The concept of adding the amplitudes of waves is known as the superposition principle. It states that at any point the resulting amplitude of two interfering waves is the algebraic sum of the displacements of the individual amplitudes.

Homework: Superposition worksheetp. 222 1-3 (just sketch) Extra p. 221 1,2 p. 222 4,5

Constructive Interference

Waves approach

Waves occupy same space

Waves diverge

Destructive Interference

Waves approach

Waves occupy same space

Waves diverge

Waves approach each other

Overlap

Resulting Wave Pattern

Remember this pattern only appears for an instant!

6.7 Mechanical Resonance

Resonance is the response of an object that is free to vibrate to a periodic force with the same frequency as the natural frequency of the object. Therefore resonance is also a transfer of energy from one object to another having the same natural frequency. If the two objects are touching, it is known as mechanical resonance.

Every object has a natural frequency at which it will vibrate. A swing’s natural frequency will depend on the length of the chains. A window rattles with its natural frequency. Bridges, propellers, blades, turbines, glasses and many types of equipment all have a natural frequency. Read p. 223-224 for examples.

If you push someone on a swing at the right time they will travel higher and higher on a swing (with the swing’s natural frequency). Think what would happen if a bridge got “pushed” at the right time over and over . . .

Tacoma narrows, singing rod, swing set, army marches

When an object vibrates in resonance with another, it is called a sympathetic vibration.

6.8 Standing Waves – A Special Case of 1 Dimensional Wave Interference

The amplitude and the wavelength of interfering waves are often different. However if the conditions are such that two waves have the same amplitude and wavelength and travel in opposite directions, then a special interference pattern known as a standing wave occurs.

Try the standing wave worksheet.

The resulting wave pattern is known as the standing wave interference pattern. Node (N): point that remains at restAnti-node: point midway between nodes where maximum constructive interference occurs

λ2

N N N N

The distance between two successive nodes in a vibrating string is 10cm. The frequency of the source is 30 Hz. What is the speed of the waves?

f = 30 Hz

λ = ?

v = ?

Distance between successive nodes is ½ λ½ λ = 10 cm λ = 20 cm

v = f λv = (30 Hz)(0.20m)v = 6.0 m/s

Hmwk. p.229 1-4

extra p.230 1-4

7.1 SOUND

Sounds are a form of energy produced by rapidly vibrating objects. Sound needs a material medium for its transmission. Sound cannot travel through a vacuum. The vibrating object causes compressions and rarefactions in the medium. A receiver senses the sound by sensing the compressions and rarefactions.

The amplitude of a sound is its loudness. The amplitude of sound in air depends on the size of the pressure changes in the air. The frequency of sound is often referred to as pitch (however this is subjective).

Young people can hear a wide range of sound, from 20 Hz to 20 000 Hz. Sounds with frequencies less than 20 Hz are infrasonic while sounds above 20 000 Hz are ultrasonic.

p. 238-241 in text

p. 241 1,2,3 extra 4

p. 242 1,4,5 extra 2,3,6,7

7.2 THE SPEED OF SOUND

Tsm

s

mV

Co)

/59.0(332

Air pressure and elevation do not significantly affect the speed of sound in air.

p. 243-246 p. 243 1-4, p.246 3-5

extra p.246 1,2,6-8

Notice any patterns?

THE INTENSITY OF SOUND

p. 247-248 p. 248 1-4, p. 249 2-4

Sound intensity is the power of sound per unit area (W/m2). Sounds can be emitted with an extremely large variance in intensity and likewise humans can sense extremely soft sounds as well as loud sounds.

The quietest whisper is about 10-12 W/m2 while a sound with an intensity of 104 W/m2 will instantly perforate an eardrum.

The decibel scale is utilized for sound intensity and gives an easy scale to judge relative intensities. The least intense sound we can hear is given the intensity of 0 dB. For every 10 dB increase in intensity the sound increases its true intensity by 10X. The scale is logarithmic so if the intensity increases by 30 dB then the true intensity has increased by a factor of 1000X.

The intensity of sound we hear depends on the power of the source and the distance between us and the source.

2/1 rI 2/1 rI

read 7.5 The Human Ear p. 249-253-will not test on parts of the human ear

read 7.6 The Reflection of Sound Waves p. 254-257-understand echoes and echo problems (remember to double distance)

-p. 257 1-4, p. 258 1-3-know echolocation and who uses it-know ultrasound applications

Not responsible for 7.7 Diffraction and Refraction of Sound Waves p. 258-260.Not responsible for section on 7.8 The Interference of Sound Waves p. 260-263.Responsible for 7.9 Beat Frequency p.264-266

-p. 266 1,2 p. 266 1-7

The Doppler Effect (p. 267-272)

The apparent changing frequency of sound in relation to an object’s motion is called the Doppler effect, named after Christian Doppler (1803-53). If a sound emitter is moving towards a listener (or vice versa) then the listener hears a higher frequency than is actually emitted. If a sound emitter is moving away from a listener (or vice versa) then the listener hears a lower frequency than is actually emitted.

The Doppler effect (Doppler shift) has been used to estimate the speed of distant stars and galaxies (using light waves) relative to our solar system. The Doppler shift is also used in police radar for speeding.

)(12svv

vff

Vs is speed of source or listener

V is speed of sound

The Mach Number is the ratio of an object’s velocity to the speed of sound.

When flying at Mach 1, an object is flying as fast as the sound it gives off. When the object emits another sound the crest will alongside the original crest so these crests pile up, producing an area of very dense air. This intense compression of air is called the sound barrier. Extra thrust is needed to break through this barrier. Objects must be designed to cut through this dense air leading to sleek and pointy shapes. At hypersonic speeds, the crests are left behind the object which constructively interfere with other crests to create a double cone. This intense acoustic pressure is called the sonic boom.

p.269 1,2 p.270 3-5 p.272 1-6

Good websites for , interference, Doppler Shift and Breaking the Sound Barrier.

http://www.phy.ntnu.edu.tw/oldjava/waveSuperposition/waveSuperposition.htmlhttp://www.kettering.edu/~drussell/Demos.htmlhttp://www.answers.com/topic/sonic-boomhttp://library.thinkquest.org/19537/java/Doppler.html

8.1 Music and Musical Notes

It’s important to realize the difference between what is music and noise. Music is sound that originates from a vibrating source with one or more frequencies (usually harmonious and pleasant). Noise on the other hand is sound that originates from a source with constantly changing frequencies and is usually not ‘pleasant’ to the ear. On an oscilloscope, noise would not have a constant wave form or pattern.

There are three main characteristics of musical sounds: pitch, loudness and quality. Each of these characteristics depends not only on the source of the musical sound, but also on the listener. Thus, they are called subjective characteristics.

Which of the following are musical and which are noise?

Pitch is the perception of the highness or lowness of a sound; it depends primarily on the frequency of the sound.

Loudness is the perception of the intensity of sound.

Sound Quality is a property that depends on the number and relative intensity of harmonics that make up the sound.

In music, a pure tone is a sound where only one frequency is heard. Musical sounds are not normally pure tones; they usually consist of more than one frequency.

In general, two or more sounds have consonance if their frequencies are in a simple ratio (simpler ratio produces more consonance). Harmonious pairs of sounds have high consonance; unpleasant pairs of sounds have high dissonance, or low consonance.

Unison is a set of sounds of the same frequency. An octave has sounds with double the frequency of the sounds in another frequency. For example, a 200-Hz sound is one octave above a 100-Hz sound.

The two common musical scales are the scientific musical scale, based on 256 Hz, and the musicians’ scale, based on 440 Hz.

p. 278 2 p. 280 3,4 p. 281 1-4

8.2 Vibrating Strings

Vibrating strings (examples?) are often used to produce musical sounds. The frequency of a vibrating string is determined by four factors: length, tension, diameter, and density. All of these factors are taken into consideration when designing stringed musical instruments, such as the piano, guitar, cello, harp, lute, mandolin, banjo and violin.

Increase length -> decrease frequency

Increase tension -> increase frequency

Increase diameter -> decrease frequency

Increase density -> decrease frequency

p. 283 1-5

Answer qualitatively!

8.3 Modes of Vibration – Qualities of Sound

When a string, stretched between two fixed points, is plucked a standing wave pattern is produced. Nodes occur at both ends. Different frequencies of varying amplitudes may result depending on how many nodes and antinodes are produced. The resulting note is the sum of all of these different vibrations of the string.

In its simplest, or fundamental mode of vibration, the string vibrates in one segment. This produces its lowest frequency, called the fundamental frequency ( fo).

If the string vibrates in more than one segment, the resulting modes of vibration are called overtones. Since the string can only vibrate in certain patterns (always with nodes at each end) the frequencies of the overtones are simple to determine.

1st overtone (f1) f1 = 2fo

These vibrations are also referred to as harmonics.

Fundamental freq. fo First harmonicFirst overtone f1 (2fo) Second harmonicSecond overtone f2 (3fo) Third harmonicThird overtone f3 (4fo) Fourth harmonic

Stringed instruments vibrate in a complex mixture of overtones superimposed on the fundamental frequency. Very few vibrating sources can produce a note free of overtones. An exception is the tuning fork, but even it has overtones when first struck. However, because the overtones disappear quickly, the tuning fork is valuable in studying sound and tuning musical instruments.

The quality of a musical note depends on the number and relative intensity of the overtones it produces along with the fundamental frequency. The quality enables us to distinguish between notes of the same frequency and intensity coming from different sources; for example, we can easily distinguish between middle C on the piano, on the violin, and in the human voice.

8.4 Resonance in Air ColumnsClosed Air ColumnsWhen a sound wave is sent down an air column (closed at one end) the end of the tube reflects the sound waves back. Certain frequencies produce standing wave patterns (through interference) that amplify the original sound. The closed end is fixed so a node is located there. The open end of the column is free to vibrate so an anti-node is located there.

Resonance first occurs when the column is (1/4) λ in length. The next possible lengths are 3/4 λ, 5/4 λ, etc. check wooden box with tuning fork

1st Resonant length

2nd Resonant Length

Sample Problem: The first resonant length of a closed air column occurs when the length is 16 cm.(a) What is the wavelength of the sound?(b) If the frequency of the source is 512 Hz, what is the speed of sound?(a) first resonant length = ¼ λ

¼ λ = 16 cm λ = 64cm

(b) v = f λ= 512 Hz (64cm)= 32 768 cm/s (327.7 m/s)

Open Air ColumnsResonance may also be produced in an open air column(open at both ends). Antinodes occur at free ends. This means the first length at which resonance occurs is 1/2 λ. Resonance will next occur at lengths of λ, 3/2 λ, 2 λ, etc.test air tubes

1st Resonant Length 2nd Resonant Length

Sample Problem: The third resonant length of an open air column occurs when the length is 50cm.(a) What is the wavelength of the sound?(b) If speed of the wave is 300 m/s, what is the source frequency?

(a) third resonant length = 3/2 λ 3/2 λ= 50 cm

λ = 0.33 m(b) f = v/ λ

= 300m/s / (0.33m)

= 9.0 x 102 Hz

p. 290 1-7, p. 292 1-7, 9