WAVES revisited…

Additional vocabulary you may need or want to remember…

Definitions• Standing Wave – a wave pattern that

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

• Node – a point in a standing wave that always undergoes complete destructive interference

• Antinode – a point in a standing wave, halfway between two nodes, at which the largest amplitude occurs

Standing waves• Count the nodes and antinodes for each standing wave

Types of waves• Bow wave - the V shaped wave produced

by an object moving on a liquid surface faster than the wave speed

• Periodic wave – a wave whose source is some form periodic motion

• Transverse wave – a wave whose particles vibrate perpendicular to the direction of a wave motion

• Longitudinal wave – a wave whose particles vibrate parallel to the direction of the wave motion

Types of waves• Shock wave - a cone shaped wave

produced by an object moving at supersonic speed through a fluid (air is a fluid)

• Sonic Boom – the sharp crack heard when the shock wave that sweeps behind the supersonic aircraft reaches the listener

SHOCK WAVES AND THE SONIC BOOMWhen the speed of a source of sound exceeds the speed of sound, the sound waves in front of the source tend to overlap and constructively interfere. The superposition of the waves produce an extremely large amplitude wave called a shock wave.

The sonic boom is produced when the plane crosses this shock wave

PSE Chapter 12 page 159Textbook Chapter 26- A musical read…

SOUND WAVES

Sound is a longitudinal wave produced by a vibration that travels away from the source through solids, liquids, or gases, but not through a vacuum.

So sound waves are also Mechanical waves- they require a medium to be transmitted

Recall that in longitudinal waves compressions and rarefactions are produced by the vibrating motion.

The compressions are regions of high air pressure while the rarefactions are regions of low air pressure. (sand/shovel analogy)

Since a sound wave consists of a repeating pattern of high pressure and low pressure regions moving through a medium, it is sometimes referred to as a pressure wave.

The above diagram can be somewhat misleading if you are not careful. The representation of sound by a sine wave is merely an attempt to illustrate the sinusoidal nature of the pressure-time fluctuations. Do not conclude that sound is a transverse wave which has crests and troughs.

When a pressure wave reaches the ear, a series of high and low pressure regions impinge upon the eardrum. The arrival of a compression pushes the eardrum inward; the arrival of a rarefaction serves to pull the eardrum outward. The continuous arrival of high and low pressure regions sets the eardrum into vibrational motion.

HUMAN EAR:The ear consists of three basic parts:

Outer ear: serves to collect and channel sound to the middle ear.

Middle ear: serves to transform the energy of a sound wave intothe vibrations of the bone structure of the middle ear and transform these vibrations into a compressional wave in the inner ear.

Inner ear: serves to transform the energy of a compressional wave within the inner ear fluid into nerve impulses which can be transmitted to the brain.

The speed of sound is independent of the pressure, frequency, and wavelength of the sound. However, the speed of sound in a gas is proportional to the temperature T.

The following equation is useful in determining the speed of sound in air

v = 330m/s + 0.6 T

Where 330 m/s is the speed of sound at 0°C, and T is the temperature in °C

The speed of sound is different in different materials.

Substance Speed   (m/s)

Air 343*

Helium 965

Water 1482

Lead 1960

Steel 5960

Granite 6000

*The speed of sound in air at room temperature (20ºC) is 343 m/s.

Applications of the speed of sound and its reflection and refraction

Sound Navigation and Ranging

Range finder –uses ultrasonicDepth/fish finder- uses clicks

10 m above a lake’s surface, a sound pulse is generated.  The echo from the bottom of the lake returns to the point of origin 0.140 second later.  The air and water temperatures are 20 C.  How deep is the lake? Speed in air:  343 m/s      Speed in water: 1482 m/s

1) Time in air?T= d/vair = 20/343 = 0.058 s

2) Time in water ?Ttotal – T air = Twater 0.140 - 0.058 = 0.082 s

3) Time to hit bottom?  0.082 / 2 = 0.041 s

4) depth? d = Vwatert = 1482 (0.041) = 60.8 m

Speed of sound = 343 m/s at 20 CSpeed of light    = 300,000,000 m/s

Rule :  See lightning,start counting seconds until sound is heard.  Divide by five to obtain distance of lightning

Example:  10 / 5 = 2 miles

The rule of “five” for lightning

Why?

Reflected waves show detail within the body.   The Fetus reflects sound much better than the fluid in which it's immersed (amniotic fluid).

Ultrasounds: Use ultrasonic sounds to image inside the body.

We detect two characteristic of sound: pitch and loudness.

Pitch is how high or low the sound seems. (use forks and wave box)

It is measured by the frequency.

The higher the frequency the higher the pitch.The lower the frequency the lower the pitch.Loudness refers to the Intensity of a sound.

It is measured by the amplitude It is measured in decibels (db) (a logarithmic scale)

What we hear depends on the frequency and the intensity of the sound.We hear frequencies in the range of 20 Hz to 20,000 Hz.

This is called the audible (or Sonic) range.

ultrasonicultrasonic

infrasonicinfrasonic

An oscilloscope can be used to “see” and measure sound waves. The oscilloscope displays period, from which frequency (pitch) may be calculated.  Amplitude (loudness) measures the energy carried in individual compressions

Relative Intensity    

Source      Intensity in Decibels

Normal breathing

10

Whisper 20

Conversation 60

Street traffic 70

Rock concert 115

Threshold of pain

120

Jet engine 140

    What we hear is also affected by

the motion of the source or us

The movie at left shows a stationary sound source. Sound waves are produced at a constant frequency and wave-fronts move symmetrically away from the source at a constant speed v. The observers at A and B, here the same pitched sound.

A B

In the movie below, the same sound source is radiating sound waves at a constant frequency in the same medium. However, now the sound source is moving to the right with a speed 100m/s

Notice listener B is receiving waves that are closer together and he hears a higher apparent frequency than before.

BA

Notice listener A is receiving waves that are further apart and he hears a lower apparent frequency than before.

DOPPLER EFFECT (PSE pg 161)

When a source of sound and/or a listener are moving, the apparent pitch of the sound changes. This phenomenon is known as the Doppler effect.

Light waves also exhibit the Doppler effect. The spectra of stars that are receding from us is shifted toward the longer wavelengths of light. This is known as the red shift.

Measurement of the red shift allows astrophysicists to calculate the speed at which stars are moving away. Since almost all stars and galaxies exhibit a red shift, it is believed that the universe is expanding.

DOPPLER EFFECT:The pitch heard by the listener is given by the following equation:

f fv v

v vSo

S

'

Units: Hz

f' is the frequency of the sound heard by the listener (observer), fS is the frequency of the sound emitted by the source,

v is the speed of sound in air, vS is the velocity of the source, and

vo is the velocity of the listener (observer).

Sign Convention: (+) for approaching velocities and (-) for receding velocities.

Example 1:A fire truck siren emits sound at a frequency of 400 Hz on a day when the speed is 340 m/s. a. What is the pitch of the sound heard when the truck is moving toward a stationary observer at a speed of 20 m/s?v = 340 m/sfS =400 Hz

vS = 20 m/s

vo = 0 m/s' o

sS

v vf f

v v

340 0400

340 20

= 425 Hz

b. What is the pitch heard when the truck is moving away from the observer at this speed?

vS = - 20 m/s ' 340 0400

340 20f

= 377.78 Hz

Example 2: A stationary source of sound has a frequency of 800 Hz on a day when the speed of sound is 340 m/s. What pitch is heard by a person who is moving from the source at 30 m/s?

v = 340 m/sfS = 800 Hz

vO = - 30 m/s

vs = 0 m/s

340 30800

340

' os

S

v vf f

v v

= 729.41 Hz

PSE Practice & Additional Problems: Sound & Music

Practice problems 1-5 of Doppler Effect on your own sheet of paper. This will be turned in later.

SHOW ALL FVWAU

Use 340 m/s for speed of sound if not given on these problems.

PSE Chapter 12 Standing Waves page 165

SOURCES OF SOUND

Sound comes from a vibrating object. If an object vibrates with frequency and intensity within the audible range, it produces sound we can hear.

MUSICAL INSTRUMENTS

Wind Instruments: Open Pipe: flute and some organ pipesClosed Pipe: clarinet, oboe and saxophone

String Instruments:

guitar, violin and piano

Percussion Instruments:Drums, bells, cymbals

As a string vibrates, it sets surrounding air molecules into vibrational motion. (called forced vibrations) The frequency at which these air molecules vibrate is equal to the frequency of vibration of the guitar string.

Forced vibrations: the vibration of an object caused by another vibrating object

Standing Waves

The nodes and antinodes remain in a fixed position for a given frequency.

There can be more than one frequency for standing waves in a single string.

Frequencies at which standing waves can beproduced are called thenatural (or resonant) frequencies.

The sounds produced by vibrating strings are not very loud. Many stringed instruments make use of a sounding board or box, sometimes called a resonator, to amplify the sounds produced. The strings on a piano are attached to a sounding board while for guitar strings a sound box is used. When the string is plucked and begins to vibrate, the sounding board or box begins to vibrate as well (forced vibrations). Since the board or box has a greater area in contact with the air, it tends to amplify the sounds.On a guitar or a violin, the length of the

strings are the same, but their mass per length is different. That changes the velocity and so the frequency changes.

(demo music box)

Demo mini-wiggler

A guitar or piano string is fixed at both ends and when the string is plucked, standing waves can be produced in the string.

Standing waves are produced by interferenceResulting in nodes an antinodes

2-antinode

Standing Waves

Since the ends are fixed, they will be the nodes.

The wavelengths of the standing waves have a simple relation to the length of the string.

The lowestlowest frequency called the fundamental fundamental frequencyfrequency has only one antinode. That corresponds to half a wavelength:

The other natural frequencies are called overtones. They are also called harmonics and they are integer multiples of the fundamental.

The fundamental is called the first harmonicfirst harmonic.

The next frequency has two antinodes and is called the second harmonicsecond harmonic.

The equation for strings is

f – frequency in hertzn – number of antinodesL – length of string in metersV – velocity in medium in meters/sec

- n can be any integer value greater than one.

Example What is the fundamental frequency of a viola string that is 35.0 cm long when the speed of waves on this string is 346 m/s?

L = 0.35 mv = 346 m/s

346

2(0.35)

= 494.29 Hz f = nv 2L

(1)

What is frequency of the third harmonic produced by this string?

f = nv 2L

346

2(0.35)

(3)= (3) 494.29 Hz = 1482.86 Hz

WIND INSTRUMENTS (PSE pg 166)

Wind instruments produce sound from the vibrations ofstanding waves in columns of air inside a pipe or a tube.In a string, the ends are nodes. In air columns the ends can be either nodes or antinodes. (demo pipes, straw and bottles)

Open at both ends pipe Closed at one end pipe

So for an Open tube

For a half-closed tube

4

Why a 4?

a) For open pipe

The overtones will be all multiples of the fundamental

n = 1, 2, 3, 4 , 5 …b) For closed pipe

The overtones will be the odd multiples of the fundamental

n = 1, 3, 5, 7, …

HARMONICSHARMONICS

Example A pipe that is open at both endsboth ends is 1.32 m long, what is the frequency of the waves in the pipe?

v = 340 m/sL = 1.32 m

= (1) (340) 2 (1.32m)

= 128.79 Hz

What if it was closed at one end?

= (1) (340) 4 (1.32m)

= 64.39 Hzf = nv 4L

f = nv 2L

Example An organ pipe that is open at both ends has a fundamental frequency of 370.0 Hz when the speed of sound in air is 331 m/s. What is the length of this pipe?

f' = 370 Hzv = 331 m/s

= 0.45 m

f = nv 2L

370 = (1)(331) 2 LL = (1)(331) 2(370)

12.1 A saxophone plays a tune in the key of B-flat. The saxophone has a third harmonic frequency of 466.2 Hz when the speed of sound in air is 331 m/s. What is the length of the pipe that makes up the saxophone?

n = 3f3 = 466.2 Hzv = 331 m/s

12.5 A pipe that is closed on one end has a seventh harmonic frequency of 466.2 Hz. If the pipe is 1.53 m long, what is the speed of the waves in the pipe?

n = 7f7 = 466.2 HzL = 1.53 m

INTERFERENCE OF SOUND WAVES: BEATS

If two sources are close in frequency, the sound from them interferes and what we hear is an alternating sound level. The level rises and falls. If the alternating sound is regular, it is called beats.

(Demo tuning forks)

The beat frequency equals the difference in frequencies between the sources.

ff beatsbeats = │ = │ff22 – – ff 11││

This is a way to tune musical instruments. Compare a tuning fork to a note and tune until the beats disappear.

CIConstructive Interference

DIDestructiveInterference

Noise canceling head phones for flights

Uses complete destructive interference

HW: WAVES WORKSHEETCW: PSE Practice problems 1-9

DUE BOC R. 28/ M.1 !!!!!!