Module 7Waves/Sound

Mechanical WAVES & SOUND

Waves are caused by a disturbance or vibration whether it’s a shifting of earth causing an earthquake or….

A vibration underneath the ocean leading to a Tsunami or….

Dropping a pebble in a pond…

Anatomy of a wave

Mechanical waves require

Particles in medium only oscillate about

Wave Equations

f = frequency measured in Hz…waves per sec

T = period measured in seconds…time for 1 complete wave to pass by

Types of waves11) TRANSVERSE) TRANSVERSE

2) LONGITUDINAL2) LONGITUDINAL

Reflection from a Boundary

Reflection and Transmission

Part of the wave energy is reflected and part is transmitted.

Part of wave energy is reflected and part is transmitted.

Which answer represents the reflection and transmission of the original waveform? Assume blue represents more dense.

Phenomena that occurs when an

DIFFRACTION

Bending around island

Explains one of reasons why AM carries better than FM. Ability to navigate obstacles better with

larger wavelengths.

ExamplesA swimmer is resting on a raft. He estimates that 3.0m separates a trough and an adjacent crest of surface waves on the lake. He counts 14 crests (how many waves?) that pass by the raft in 20s. How fast are the waves moving?

The speed of sound in water is 1498m/s. A sonar signal is sent from a ship at a point just below the water surface and 1.80s later the reflected signal is detected. How deep is the ocean beneath the ship?

What is period and amplitude of wave if the y-axis is measured in meters?

H

E

I

G

H

T

REFRACTION

Wave slowing down…wavelength decreases, not frequency

Boundary between media

Submarines & refraction• Because of thermal

gradients (layers of different temperature water), SONAR waves will refract or bend and miss hitting or detecting a submarine.

• In essence, the submarine can hide in a ‘blind spot’.

Wave Interference

When 2 or more waves overlap, they interfere (exist at same pt in space) to either add or subtract in amplitude

2 Types of wave interference

1) CONSTRUCTIVE INTERFERENCE

2) DESTRUCTIVE INTERFERENCE

Example of Superposition(waves interfering)

As the two wave

pulses overlap, the sum

of the two waves yields

a larger wave for a

moment in time.

Application of D.I.Earpiece of the headphone has a microphone (points away from ear). Microphone records the ambient noise that's coming in the direction of your ear. The computer circuitry in the headphone then plays the recorded noise 180o out of phase to cancel it out.

Speed of waves on string or wire

A wave moves at 24m/s when the wire is disturbed by a mechanical oscillator. Mass of 3.0kg hangs from the end of the string.

a) Find the linear mass density of the wire.

b) If the wire has a mass of 50g, determine its length.

A telephone cord is 4.0m long and has a mass of 0.20kg. If a wave pulse moves from one end to the other in 0.10s, find the tension in cord.

Example #2

Standing Waves

String is plucked in middle sending waves in opposite directions

Waves reflect off wall travel back towards each other.

Standing Wave Pattern

Standing Wave Modes

If a string is continually shaken at the right frequency you can establish standing waves. n = 1

n = 2

n = 3

n = 4L = fixed length

Harmonics refer to the mode of the standing wave

f1= fundamental

f2 = 2f1

f3= 3f1

When a guitarist slides their finger and decreases the effective length of vibrating string to half, what happens to the frequency of the note?

Decreasing length to half increases frequency by factor of 2.

A standing wave is set up on a single string, as shown. The two fixed ends are attached to walls 73 cm apart.

a) What is the wavelength of the traveling waves on the string which make up this standing wave?

b) If waves on the string travel at a speed of 15m/s, what is the frequency of the standing wave?

c) What harmonic of vibration is shown?

d) What is the fundamental frequency of vibration?

–Resonance occurs when a vibration is forced upon an object WHERE the vibration has the SAME FREQUENCY as the natural frequency of the object.

RESONANCE

Many objects have a natural frequency or fundamental mode they vibrate in if disturbed.

This causes resonance where the object starts to ‘rattle’ and standing waves build within object making large amplitudes.

Blowing over neck of bottle or running finger over edge of wine glass creates resonance. You hear the STANDING WAVE.

Longer objects tend to have a lower resonant frequency…vibrate or oscillate slower

Shorter objects tend to have higher resonant frequencies

Tines for music box

Sound

Now consider your ear

Eardrum vibrates

Nerves tell brain “sound!”

Sound waves are longitudinal

Sound travels through the air through a series of compressions and rarefactions.

Sound travels at different speeds in different materials. Sound typically travels faster in a solid than in a liquid and faster in a liquid than a gas.

The denser the medium, the faster sound will travel. This seems to contradict what happens with 2 diff ropes tied together (transverse waves)

The higher the temperature, the faster the particles of the medium will move and the faster the particles will carry the sound.

With transverse waves, the particles are made to move a greater distance whereas longitudinal or compressional waves is a very slight movement coupled with fact that particles are close together in more dense material

Speed of sound

Speed of sound in AIR depends on temperature:

Room temperature is considered to be 20oC

Speed of sound is about 750mph (Mach 1) at room temperature

The pitch of a sound wave is directly related to frequency.

A healthy human ear can hear frequencies in the range of 20 Hz to 20,000 Hz. Humans cannot hear below 20 Hz. Sounds below this frequency are termed infrasonic.

Sounds above 20,000 Hz are termed ultrasonic. Some animals, such as dogs, can hear frequencies in this range in which humans cannot hear…Mosquito ring tone

Fog-horns are low pitched…why?Male vs female vocal chords?

Standing waves in air columns

• Resonance can be achieved for sound waves

• This can occur for a pipe open at only one end or open at both ends.

• This is the principle behind wind instruments.

Pipes open at both ends

• Pipes open at each end are similar to strings and exhibit all-numbered harmonics where

Note that the waves are NOT transverse. These pics show the displacement of air.

v = speed of sound

½ λ

1 λ

Pipes closed at one end• Pipes closed at one end only exhibit odd-

numbered harmonics where

¼ λ

¾ λ

Example:The Length of an Organ Pipe

An organ pipe open at both ends sounds its 2nd harmonic at a frequency of 523 Hz.What is the length of the pipe from sounding hole to end if the air temperature is 23oC?

ExampleA piano string has length 1.15m and mass 20g. It is under tension of 6300N. If its fundamental sets an 2.0m long open tube into resonance at its 3rd harmonic, find the temperature of the air.

Find the harmonic number

What fraction of wavelength is in the tube?

A tube open at one end is 1.0m long. Speed of sound is 345m/s with a resonant frequency of 431.25Hz inside tube.

Example

DOPPLER SHIFT

Consider a stationary water spider doing pushups in a pool of water.

Circular waves travel outward in all directions at constant speed and wavelength at the frequency the spider is moving up and down.

Observers at points ‘A’ and ‘B’ would BOTH detect the SAME frequency of waves passing by them.

Spider is NOT moving

What IF spider starts to move across the water while still bobbing up and down…how will that change the waves produced?

If spider starts to move to the right while still making waves, then it looks like…

Note how waves get shorter on right side and longer on left side.

• DOPPLER SHIFT involves the change in frequency or wavelength from a source due to motion between source and observer. You hear lower f as source leaves you & higher as it approaches you.

Observer ‘A’ detects LESS waves per second. ‘B’ detects MORE waves per second.

‘A’ measures longer wavelength than ‘B’.

Doppler formula

Use top signs for approaching

Applications of Doppler

• Ultrasound (babies + blood flow in artery)

• Weather radar• Police radar• Astronomy (blue shift

vs red shift) for rotation, movement of stars, galaxies

example1 A car approaches at 25m/s sounding its

horn while you stand on a corner. The horn sounds like 150Hz to you. Speed of sound is 343m/s. What is the actual frequency of the horn?

Determine frequency heard by person driving at 15m/s away from blowing factory whistle (800Hz) if the air temperature is 16oC.

example2

Beats

Beats result from interference between 2 waves of SIMILAR frequency

The waves demonstrate C.I. and D.I. periodically

Beats (block rockin)

Waves are in step at arrows

Examples

A piano tuner uses a tuning fork with a frequency of 330 Hz to tune a piano string. When he strikes the tuning fork and strikes the key of the piano that vibrates this string he notices a beat occurring every 1.50 s. How far off in frequency is the piano string?

A source emits a sound of wavelengths 3.15m and 3.50m in air at 20oC. How many beats per second will be heard?

Example

A guitar string is sounded with a 440Hz tuning fork, a beat frequency of 5Hz is heard. When the same string is sounded along with a 436Hz tuning fork, the beat frequency is 9Hz. What is the frequency of the string?

Sonic Boom

Object moving at subsonic speed

Object moving at sonic speed, Mach 1

Object moving supersonic.

At the speed of sound (Mach 1), the vehicle is traveling fast enough to catch up with all of the forward moving sound waves, forming a strong pressure wave normal to the vehicle. This is the pressure wave that destroyed many aircraft before the flight of the X-1 in 1947.

If a moving source of sound moves at the same speed as sound, then the source will always be at the leading edge of the waves which it produces.

If the vehicle has the proper design and has enough power to exceed the speed of sound, it can out run the shock wave which then bends back to form a strong shock cone. When this cone reaches observers on the ground or at track side, the sudden change in pressure as the wave passes causes a sonic boom. Instead of these compressional regions (high pressure regions) reaching you one at a time in consecutive fashion, they all reach you at once.

As the vehicle passes through Mach 1 the pilot or driver senses a sudden silence because they are outrunning all air noise.

The circular lines represent compressional wavefronts of the sound waves. Notice that these circles are bunched up at the front of the aircraft. This phenomenon is known as a shock wave.

Ducks fly in V formations with the lead duck setting up pressure vortices in the air in a V shaped wave. The other ducks in the formation ride the V wave and use only one half of the energy to fly that the lead duck must use.