Unit 4 Waves and Sound

Lesson35.notebook May 27, 2013

Unit 4 Waves and SoundWaves and Their Properties

Today's goal: I can explain the difference between transverse and longitudinal waves and their properties. Waves are a disturbances that transfer energy over a distance. The sources of these disturbances occur from vibrations. For example:

Earthquakes cause the ground to vibrate. A tuning fork's tines vibrate. A plucked string on a guitar or a piano string vibrate.

The vibration source supplies the energy that is transferred through the medium as a wave.

A medium is the same as saying "the composition or material" a wave is passing through. It could be water, air, steel, wood, ...

There are two types of vibration.

General properties of vibrations:A cycle is one complete oscillation of vibration. (ie. The object returns to its original position in the oscillation.)

Frequency is the number of cycles per second. Formula:

Period is the time required for one cycle to occur. Formula:

The relationship between frequency and period is:

Longitudinal vibration occurs when an object oscillates (moves back and forth) parallel to its natural rest position.

Transverse vibration occurs when an object oscillates (moves back and forth) perpendicular to its natural rest position.


Transverse versus Longitudinal VibrationsLets use an example from a "reallife" experience to analyze.

Transverse Vibration Longitudinal Vibrationeg. The girl on the swing. eg. Mass on a hanging spring.

Lets analyze the girl on the swing or the Transverse vibration.


A better representation: http://www.schulphysik.de/suren/Applets.html

Lets analyze the oscillating spring or the Longitudinal vibration.

http://www.schulphysik.de/suren/applets.html


A better representation: http://www.schulphysik.de/suren/Applets.html

Example: Longitudinal vs TransverseSketch a wave with an amplitude of 10 units and a period of 12 seconds.



Drawing waves in 2 D

Example: A mass hung from a spring vibrates 15 times in 12 seconds. Calculate:A) The frequency. B) The period of vibration.

Example: The frequency of a wave is 6.0 x 101 Hz. Calculate the period.

Example: A child on a swing has an amplitude of 1.2 m. What total distance does the child move through horizontally in 3 cycles?


Universal Wave Equation

We know from kinematics that the velocity of an object in a constant state of motion can be calculated by:

Now if we introduce some of our "new" terminology into the mix:

Example: Calculate the speed of sound leaving the tuning fork at a frequency of 125 Hz, if the wavelength of one cycle is 275 cm.

Example: Find the velocity of the wave if the wavelength is 75 cm and the period is 2 minutes.

Homework:

page 473, #23 32


Transmission and Speed of Sound

Today's goal: I can explain how sound is transmitted through a medium and how realworld applications (ie. Mach number) are connected with the concept.

Sound is a longitudinal wave which requires a medium to travel in. This would mean that...

Sound is a form of energy transfer. In this situation we are transferring energy created from vibration to "sound" energy. For the energy to travel it requires a medium and the medium will determine the speed of sound.

Why?We know from the kinetic molecular theory that...

Some examples of different mediums:Medium Density (kg/m3) Speed of sound (m/s)Air 1.29 331Water 1000 1498Copper 8930 3800Iron 7800 5000

Page 446 in textbook lists several other mediums.

In general, the stiffer the material, the faster the speed of sound in the medium.

Even within air itself, there will be a variance of velocity as with all materials, as the temperature of the medium increases, the distance between particles increases making the transmission of energy less efficient. A simple class example:


The relationship:

Through experimentation physicists have determined that the temperature affects the velocity of sound in air by 0.6 m/s /C. Therefore:

v = 332 + 0.6T, where:

Example: Find the velocity of sound in air when the mean temperature is 30 degrees Celsius.

Example: If you see a lightning strike and then 5 seconds later you hear the thunder, determine how far away the lightning was if the temperature this evening is 18 degrees Celsius.


What is SONAR? SOund Navigation And Ranging

Bats and dolphins use this to determine how far they are from an object. They emit sounds at a high rate (130kHz range). These waves bounce off any objects which they happen to come into contact with. By seeing how long it takes for the wave to come back to them they can determine how far the object is.

The Mach NumberThe "Mach Number" is simply a comparison of velocity with respect to the velocity of sound in air under current conditions.

For example, if the temperature is 0 degrees Celsius then,Mach 1 = 332 m/s Mach 2 = 2 x 332 Mach 3 = 3 x 332

= 664 m/s = 996 m/s

Example: Determine the Mach Number of a plane flying at 850 m/s in an air temperature of 5 degrees Celsius.


Example: A plane is travelling at Mach 1.8 or 500 m/s. What is the air temperature?

Homework

3U Page 474, #33 48


The Sound Barrier

Today's goal: I can explain phenomena like the sound barrier, sound intensity and the Doppler effect work using proper terminology.

The term "sound barrier" describes the build up of sound waves in front of a fast moving object. This happens as the object's speed increases and begins to "catch" its own sound waves.

Stationary Object Moving Object Fast moving object

As an object reaches the sound barrier (approx. 332 m/s) there is an enormous pressure buildup as the air particles have been compressed very close together. In order to break through this pressure barrier an large amount of energy is required.

The aviation industry never had a shortage of energy, however, maintaining control was a major issue. Most planes that reached the sound barrier were not able to be controlled. Not until the advent of the "delta wing" or "sweep wing" design was the sound barrier safely crossed.

The Sonic BoomThe "sonic boom" or "sonic shock wave" is the result of an object travelling faster than the speed of sound and leaving a "pressure wake" behind it. The wake spreads out similar to the wake of a boat until it reaches ground level for the observer. http://www.explorelearning.com/index.cfm?method=cUser.dspLoginJoin


The four stages:v = 0 m/s v < mach 1

v = mach 1 v > mach 1

Sound IntensitySimilar to water waves dissipating as they move away from a source (dropped pebble) so do sound waves.

The intensity (I) of a sound wave is defined as the rate of power (P) that passes through an area (A) perpendicular to the wave's direction.

Therefore, I = P / A however in the "realworld" is 3D so:

Comparing Two intensities:


Sound is measured using the Decibel System which works in magnitudes of millions for each range. To make the numbers manageable and also result in a linear relationship, physicists use "logarithms" to analyze sound intensity.

Just a bit of grade 12 math to help put things in perspective:

β = 10log(I1) Δβ = 10log(I1/I2)

Example: Given a sound source's intensity is 5.0 x 106 W/m2 determine the intensity if:A) The distance from the source is doubled.B) The distance from the source is quartered.

Example: How many times more intense is a motorcycle (100 dB) than a passing train (70 dB)?


Example: A passing train produces sound at 70 dB measured 3 m away. How far must you stand so that the sound level is 50 dB?

The Doppler EffectThe Doppler Effect is a physical phenomena that everybody has experienced at one point or another in their lifetime. The following slides introduce and discuss the topic.

Case 1: The sound is moving toward you.

f1 ‐ frequency from hornvs ‐velocity of soundvo ‐ velocity of object

f2 = frequency heard


Case 2: The sound is moving away from you.

f1 ‐ frequency from hornvs ‐velocity of soundvo ‐ velocity of object

f2 = frequency heard

Example: A taxi is approaching Dylan at a velocity of 20 m/s while honking its horn. Calculate the frequency of the sound heard by Dylan if the horn has a frequency of 500 Hz and the speed of sound is 344 m/s when:A) The taxi is approaching Dylan.B) The taxi is driving away from Dylan.

Homework:page 475 #49, 56 58, 61, 62, 64 71


Sound Waves and Matter

Today's goal: I can explain how sound waves are absorbed, transmitted and/or reflected through matter and apply the knowledge to different situations.

All forms of waves can be absorbed, transmitted or reflected.

Absorption

Absorption is the process where sound's energy is quickly dissipated by being transformed into other forms of energy.

Engineers have accomplished this by using absorptive materials (cork, heavy cloth, etc...) and odd looking 3D "baffles" that reflect the sound until the waves get absorbed.

Example: Wall cross section

Transmission

Transmission is the passing of sound energy from one medium to another at the medium boundary.

Using a ratio of velocity for each medium and the Universal Wave equation we find that:


Example: A sound wave travelling through air (v = 332 m/s) and with wavelength of 0.75 metres hits a steel wall. What is the wavelength that is transmitted into the steel wall if speed of sound in steel is 5000 m/s?

Reflection

Sound energy can hit a surface and be reflected back onto itself. However, the reflected wave has its phase shifted by 1/2λ. There are two types of reflection:

Fixed End Reflection Free End Reflectionhttp://www.schulphysik.de/suren/Applets.html



Waves at a boundary (ex. Air to Steel)

Homework:

page 512 #13


The Principle of Superposition

Today's goal: I can explain and apply the concept of superposition in terms of wave interference and predict the resulting destructive interference.

When you performed the "wave property" investigation you saw in some of you results "dark" or "black" lines created. For example:

http://www.schulphysik.de/suren/Applets.html

Interference

Constructive Interference Multiple waves are in a cycle which enhances the amplitude of the crest or trough.

Destructive Interference Multiple waves are in a cycle which decreases the amplitude of a crest or trough.





Homework:

Complete the handout


Characteristics of Sound

Today's goal: I can explain the various characteristics of sound and apply them to realworld phenomena (ie. beat frequency, nodes, etc...).

An oscilloscope transforms sound energy to a graphical representation of the wave. Example:

Frequency and Sound

Amplitude and Sound

Interference and Beats

When two waves with different frequencies result in both constructive and destructive interference it creates "beats".

A "beat" is a full cycle of loudness.

Graphing Calculator: y=5sin(30πx)

Tuning Forks:

Beat Frequency is |f2 f1| and fbeats = N / Δt


Example: When a tuning fork with a frequency of 512 Hz and a tuning fork of unknown frequency are heard together for a period of 4 seconds there are 20 beats. What is the possible frequency of the second tuning fork?

Standing Waves

A standing wave occurs when a wave reflects back on itself with the same frequency, wave length and speed. The resulting wave has a particular pattern caused by a special kind of interference.


wave reflected wave

Calculating Internodal Distance

dn = (1/2)λ

Example: A standing wave occurs in a duck pond when a duck repeatedly tries to jump for food. A) If there are nodes at every 38 cm, what wavelength of wave is the duck creating? B) If the wave speed in the pond is 0.95 m/s, how often is the duck jumping?


ResonanceEvery object is vibrating at a particular frequency. This is called the objects natural frequency.

Frequency Diagram Physic Term Music Term

Mechanical resonance is the vibrating response of an object to a periodic force from a source that has the same frequency as the natural frequency as the natural frequency of the object.

Example: The Tuning Forks


Real Life Application: The Tacoma Narrows Bridge

Less "disastrous" examples of resonance:

1) Rocking a car when stuck in the snow.

2) Pushing a child on a swing.


3) The baseball bat

Homework:page 512 #17, 18page 514 #37 39


Acoustical Resonance

Today's goal: I can explain concepts of acoustical resonance, specifically, how it applies to open and closed ended air columns.

Acoustical Resonance is the process responsible for sound waves that come from various instruments, each tuned to a particular natural frequency. When played a standing wave is created or "played".

Wind instruments are elaborate air columns in which a standing wave is formed. For example:

Open Ended

Closed Ended

Using a chart we can investigate the general properties of open and closed air columns:

Open ended instrument:

Resonant Length Diagram Number of

nodes Length of column in terms of wavelength

`


Closed ended instrument:

Resonant Length Diagram Number of

nodes

Length of column in terms of wavelength

`

Example: An air column that is open at both ends is 1.5 m long. A specific frequency is heard. If the air temperature is 20 degrees C, what is the longest possible wavelength and its frequency to cause resonance?


Example: A closed air column resonantes at two consecutive lengths (fundamental frequencies) of 94 cm and 156 cm. If the air temperature is 20 degrees C, determine the resonant frequency of the air column.

Homework:

page 512 #19 26


Woodwinds and Stringed Instruments

Today's goal: I can explain how various wind and stringed instruments work using concepts discussed in the unit using proper terminology.

Recall:

Open Ended: L =

Closed Ended: L =

If velocity remains constant and we apply the universal wave equation:

Frequency Wavelength Pitch

With air columns, we have to keep the frequency constant so:

Length of column Pitch

The Trombone


The Flute

The Guitar

Four variables affect the frequency of a string with stringed instruments:

1) Length: Inversely proportional

2) Tension: Directly proportional (square root)

3) Diameter: Inversely proportional

4) Density: Inversely proportional (square root)


Example: A guitar player changes the string length from 0.9 m to 0.4 m. It has a new frequency of 500 Hz. Determine the original frequency.

Example: Determine the resulting frequency if the string on a guitar is changed such that the heavier wire is used (density and diameter are doubled), the length is 10% shorter, the tension is tripled.

Homework:

The handout

Documents

Unit 4 Waves and Sound