and Waves Sound
AP Physics B
Aim: What are wave properties?
Objectives a) Sketch wave graphs and determine the amplitude, wavelength, and frequency b) Relate wavelength, frequency, and velocity for a wave. c) Explain the Doppler effect for sound. d) Describe reflection of a wave from the fixed or free end of a string. e) Describe qualitatively what factors determine the speed of waves on a string and the speed of sound.
What is a wave
A WAVE is a vibration or disturbance in space.
A MEDIUM is the substance that all SOUND WAVES travel through and need to have in order to move.
Two types of Waves
The first type of wave is called Longitudinal.
Longitudinal Wave - A fixed point will move parallel with the wave motion 2 areas Compression- an area of high molecular density and pressure Rarefaction - an area of low molecular density and pressure
Two types of Waves
The second type of wave is called Transverse.
Transverse Wave - A fixed point will move perpendicular with the wave motion. Wave parts-crest, trough, wavelength, amplitude, frequency, period
Cyclical Motion
Period ()= the time for one wave cycle to be completed
=1/f Unit: Seconds
Frequency (f )=the number of cycles per unit time
f=cycles/time OR Unit: Hertz (Hz)
f=1/
1Hz=1cylce/1second
Frequency:
Sound Waves: PITCH, NOTE high frequency high note Light Waves: COLOR high frequency more "blue" ROYGBIV
Wave Speed
You can find the speed of a wave by multiplying the wave's wavelength in meters by the frequency (cycles per second). Since a "cycle" is not a standard unit this gives you meters/second.
Example
A harmonic wave is traveling along a rope. It is observed that the oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along a rope in 10.0 s . What is the wavelength?
cycles 40 f = = = 1.33 Hz sec 30 x 4.25 v= = = 0.425 m/s t 10 vwave vwave = f = = 0.319 m f
Sound Waves
Sound Waves are a common type of standing wave as they are caused by RESONANCE. Resonance when a FORCED vibration matches an object's natural frequency thus producing vibration, sound, or even damage.
One example of this involves shattering a wine glass by hitting a musical note that is on the same frequency as the natural frequency of the glass. (Natural frequency depends on the size, shape, and composition of the object in question.) Because the frequencies resonate, or are in sync with one another, maximum energy transfer is possible.
http://www.5min.com/Video/The-Original-Tacoma-Narrows-Bridge-Collapse-of-1940-119995718
RESONANCE
An oscillating system is in resonance with some driving force whenever the frequency of the driving force matches one of the natural frequencies of the system; the system responds with a large A.
Doppler Effect
Doppler Effect
Doppler effect occurs for all types of waves, water, sound and even light. This is how we know the universe is expanding.
SITUATION 3 Moving Source; Stationary Observers
As the source moves a distance vS (T=1/f period of wave) toward O1 there is a decrease in the wavelength of sound by a quantity of vs . The shortened wavelength ' becomes
' = vsT
The frequency f' of sound wave heard by O1 increases as given by,
(6)
Moving Source and Observer
Wave Barriers
The object is moving at the speed of waves in the medium.
Shock Waves
The source is moving faster than the wave speed in the medium. A shock wave is formed and it is very difficult to break through the previous wave barrier. These waves produce sonic booms.
19
Doppler Example
Intelligence tells you that a particular piece of machinery in the engine room of a Victor III submarine emits a frequency of 320 Hz. Your sonar operator hears the machinery but reports the frequency is 325 Hz. Assume you have slowed to a negligible speed in order to better hear the submarine.
Is the VIII coming toward you or moving away from you? Assuming the Victor is either moving directly toward or away from you, what is his speed in m/s?
Aim: What are standing waves?
Objectives Describe a) reflection of a wave from the fixed or free end of a string. b) Describe qualitatively what factors determine the speed of waves on a string and the speed of sound.
Standing Waves
A standing wave is produced when a wave that is traveling is reflected back upon itself. There are two main parts to a standing wave: Antinodes Areas of MAXIMUM AMPLITUDE Nodes Areas of ZERO AMPLITUDE.
Standing Waves
Occurs when a wave reflects upon itself and interference causes the pattern Nodes remain stationary Anti nodes-occur half way between nodes
Sound Waves
The production of sound involves setting up a wave in air. To set up a CONTINUOUS sound you will need to set a standing wave pattern. Three LARGE CLASSES of instruments Stringed - standing wave is set up in a tightly stretched string Percussion - standing wave is produced by the vibration of solid objects Wind - standing wave is set up in a column of air that is either OPEN or CLOSED Factors that influence the speed of sound are density of solids or liquid, and TEMPERATURE
FIXED ENDS
fundamental/1st harmonic 2nd harmonic 3rd harmonic 4th harmonic Normal modes
2L n = n
n = 1, 2,3,K n = 1, 2,3,K T v=
v v fn = = n n 2L
Speed of a wave in a wire
Depends on: 1. linear mass density () = mass/length (kg/m) 2.Tension in string (T)
Closed Pipes
Have an antinode at one end and a node at the other. Each sound you hear will occur when an antinode appears at the top of the pipe. What is the SMALLEST length of pipe you can have to hear a sound?
You get your first sound or encounter your first antinode when the length of the actual pipe is equal to a quarter of a wavelength. This FIRST SOUND is called the FUNDAMENTAL FREQUENCY or the FIRST HARMONIC.
Closed Pipes Harmonics
Harmonics are MULTIPLES of the fundamental frequency.
In a closed pipe, you have a NODE at the 2nd harmonic position, therefore NO SOUND is produced
Closed Pipes Harmonics
In a closed pipe you have an ANTINODE at the 3rd harmonic position, therefore SOUND is produced. CONCLUSION: Sounds in CLOSED pipes are produced ONLY at ODD HARMONICS!
Closed at one end:
v fn = n 4L
n = 1,3,5,K
Open Pipes
OPEN PIPES- have an antinode on BOTH ends of the tube. What is the SMALLEST length of pipe you can have to hear a sound?
You will get your FIRST sound when the length of the pipe equals one-half of a wavelength.
Open Pipes Harmonics
Since harmonics are MULTIPLES of the fundamental, the second harmonic of an "open pipe" will be ONE WAVELENGTH.
The picture above is the SECOND harmonic or the FIRST OVERTONE.
Open pipes Harmonics
Another half of a wavelength would ALSO produce an antinode on BOTH ends. In fact, no matter how many halves you add you will always have an antinode on the ends
The picture above is the THIRD harmonic or the SECOND OVERTONE. CONCLUSION: Sounds in OPEN pipes are produced at ALL HARMONICS!
STANDING WAVES IN AIR COLUMNS
Open at both ends:
v fn = n 2L
n = 1, 2,3,K
Example
The speed of sound waves in air is found to be 340 m/s. Determine the fundamental frequency (1st harmonic) of an open-end air column which has a length of 67.5 cm.
v = 2lf 340 = 2(0.675) f f = 251.85 HZ
Example
The windpipe of a typical whooping crane is about 1.525-m long. What is the lowest resonant frequency of this pipe assuming it is a pipe closed at one end? Assume a temperature of 37C.
[(0.6)(37)] + 331 = v = 4lf v = 4(1.525) f f =
57.90 Hz
353.2 m/s
Example 3
A steel wire in a piano has a length of 0.700 m and a mass of 4.300 103 kg. To what tension must this wire be stretched in order that the fundamental vibration correspond to middle C (fC = 261.6 Hz on the chromatic musical scale)?
Example 4
Two pieces of steel wire with identical cross sections have lengths of L and 2L. The wires are each fixed at both ends and stretched so that the tension in the longer wire is four times greater than in the shorter wire. If the fundamental frequency in the shorter wire is 60 Hz, what is the frequency of the second harmonic in the longer wire?