Mechanical Waves & Sound

Wave Motion

Waves are caused by

A vibration underneath the ocean can lead to a Tsunami

Wave anatomy:

• Amplitude, A = Wavelength, λ =

• Frequency, f = Period, T =

• Wave velocity, v

Types of Waves: Transverse and Longitudinal

Transverse

Longitudinal

Reflection of Waves

Reflection and Transmission of Waves

When wave enters NEW medium,

Phenomena that occurs when an obstacle or opening causes wave to change direction and bendbend around it.

DIFFRACTION

As the opening gets smaller, diffraction becomes more apparent.

A 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 that pass by the raft in 20.0 s. How fast are the waves moving?

REFRACTION

Wave slowing down…

Why?

Boundary between media

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

Destructive vs Constructive

Speed of waves on string/wire Speed of wave is

determined by the tension and linear mass density of string

A wave moves at 24m/s when the wire is plucked. Mass of 3.0kg hangs from the end of the string.

Find the mass per unit length of wire.

Standing Waves

String is plucked in middle sending waves in opposite directions

Waves reflect off wall travel back towards each other.

Standing Wave Pattern

If waves of the SAME FREQUENCY & AMPLITUDE interfere, a standing wave will emerge.

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

n = 2

n = 3

n = 4

Harmonics refer to the mode of the standing wave

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

a) If the string has a tension of 11.25N and linear mass density of 0.05kg/m, what is the frequency of the standing wave?

b) What is the fundamental frequency of vibration?

RESONANCE

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

Sound waves are longitudinal

Sound waves REQUIRE a medium as do all mechanical waves.

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.

Speed of sound

Speed of sound in AIR depends on temperature:

Room temperature is considered to be 20oC

Standing waves in air columns

• Resonance can be achieved for sound waves as it was for strings.

• 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

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

numbered harmonics where

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 (both ends) into resonance at its 3rd harmonic, find the temperature of the air.

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.

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

Doppler formula

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

Example

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?

Beats

Beats result from interference between 2 waves of SIMILAR frequency

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

Beats

Waves are in step at arrows

Example

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.