Lecture 19 Waves
Types of waves Transverse waves Longitudinal waves
Periodic Motion Superposition Standing waves Beats Waves
Waves: •Transmit energy and information •Originate from: source oscillating
Mechanical waves Require a medium for their transmission Involve mechanical displacement •Sound waves •Water waves (tsunami) •Earthquakes •Wave on a stretched string
Non-mechanical waves Can propagate in a vacuum Electromagnetic waves Involve electric & magnetic fields •Light, • X-rays •Gamma waves, • radio waves •microwaves, etc Waves
Mechanical waves •Need a source of disturbance •Medium •Mechanism with which adjacent sections of medium can influence each other
Consider a stone dropped into water. Produces water waves which move away from the point of impact
An object on the surface of the water nearby moves up and down and back and forth about its original position Object does not undergo any net displacement “Water wave” will move but the water itself will not be carried along. Mexican wave Waves Transverse and Longitudinal waves Transverse Waves Particles of the disturbed medium through which the wave passes move in a direction perpendicular to the direction of wave propagation Wave on a stretched string Electromagnetic waves •Light, • X-rays etc
Longitudinal Waves Particles of the disturbed medium move back and forth in a direction along the direction of wave propagation.
Mechanical waves •Sound waves Waves
Transverse waves
Pulse (wave) moves left to right Particles of rope move in a direction perpendicular to the direction of the wave
Rope never moves in the direction of the wave
Energy and not matter is transported by the wave Waves Transverse and Longitudinal waves
Transverse Waves
Motion of disturbed medium is in a direction perpendicular to the direction of wave propagation Longitudinal Waves
Particles of the disturbed medium move in a direction along the direction of wave propagation. F m Netrestoring force F r by the spring ; releaseda force (F Object compressed attached to spring. Spring Vibrational motion simple simple harmonic motion to x:undergoes object proportional
or stretched a(x) andthen or stretched smalldistance
x x
m
F
r
m Waves
r r
) is exerted on the object ) isexertedontheobject of time traces out a Motion of mass as a function Displacement
kx F r Fx sine wave r
time
Waves
Fr kx Hooke’s law
Not only applies to springs Wavelength identical points on the ( pointswaveon identical a trough relative to the normal levelto the relative normal a trough Amplitude crests crests move. Wave Velocity Object vibrating with single frequency Displacement versus time Displacement(or distance) Single wave frequencycharacteristics Displacement crest Trough l
: Max height of a crest of of a crest depth or : Max height
: Distance between two successive: Distancebetween v
1 v f
: at whichthe wave Velocity Waves s t vt s vf l
l λ
)
l amplitude l
vT Time or distance
Waves
Sound A plucked string will vibrate at its natural frequency and alternately compresses and rarefies the air alongside it.
rarefaction compression
Density of Air of Density
Compressed air [increased pressure] Rarefied air [reduced pressure] Air molecules move away from high pressure region >>>>>> setting up longitudinal wave organised vibrations of air molecules>> sound Waves
Sound waves-(variation in air pressure) can cause objects to oscillate
Example: ear drum is forced to vibrate in response to the air pressure variation Waves
Wave characteristics
Frequency of waves
• Frequency (f) of a wave is independent of the medium through which the wave travels. –it is determined by the frequency of the oscillator that is the source of the waves.
Speed of waves •The speed of the wave is dependent on the characteristics of the medium through which the wave is traveling.
Wavelength
•The wavelength (l) is a function of both the oscillator frequency and the speed (v) of the wave such that vf l Waves
Superposition Two or more waves travelling through same part of medium at the same time What happens?
Adding waves sum of the disturbances of the combined waves
If amplitude increases: constructive interference
If amplitude decreases: destructive interference
Vocal sounds .combination of waves of different frequencies
Voice individually recognisable Waves Superposition Simple case: Addition of two waves with same wavelength and amplitude
In step: Added, crest to crest (trough to trough)
wave 1
wave 2
time displacement
resultant
Out of step: Added, crest to trough
wave 1
wave 2
resultant Waves Standing waves Two waves (same frequency) travelling in opposite directions Waves reflected back from a fixed position
Fundamental
1st Overtone
2nd Overtone
3rd Overtone
Nodes; positions of no displacement Antinodes; positions of maximum displacement
Distance between successive nodes (antinodes) = l Applications 2 Microwave ovens Musical instruments Waves Standing waves Fundamental
1st Overtone
2nd Overtone
3rd Overtone
String held tightly at both ends Only certain modes of vibration allowed Only certain wavelengths allowed Standing wave must have node at either end
Length of string may be changed to get other wavelengths Example: guitar fingering Changing the vibrating length Standing waves: organ pipes Waves
Waves on a stretched string
Consider a vibrating string;
Wave speed is a function of •tension of the string •Mass per unit length
T Wave speed v mL/
T is the tension m is the mass of the string L is the length of the string Waves
Example What is the frequency of the fundamental mode of vibration of a wire of length 400mm and mass 3.00 g with a tension of 300N. T Wave speed vfl mL/
300Nm (400 103 ) v 3 103 kg v(4 104 ) m 2 s 2 200 ms 1
vf l l= 2L v200 ms1 f 250 Hz 2Lm 2 0.4 Waves
Superposition
Simple case: Addition of two waves with same frequency and amplitude
Beats If the two waves interfering have slightly different frequencies (wavelengths), beats occur.
In step (in phase) In step (in phase)
Out of step (out of phase) Waves Beats If the two waves interfering have slightly different frequencies (wavelengths), beats occur.
Wave 1
Wave 2
resultant Waves get in and out of step as time progresses Result- • constructive and destructive interference occurs alternately •Amplitude changes periodically at the beat frequency Beat frequency = fb = f1-f2 Absolute value: beat frequency always positive Waves
Beats fb = f1-f2
If frequency difference = zero No beats occur
Wave 1
Wave 2
resultant Waves Beats Beats can happen with any type of waves Sound waves Beats perceived as a modulated sound: loudness varies periodically at the beat frequency Application Accurate determination of frequency
Example Piano tuning Adjust tension in wire and listen for beats between it and a tuning fork of known frequency
The two frequencies are equal when the beats cease. Easier to determine than when listening to individual sounds of nearly equal frequencies
f1 = 264Hz f2 = 266 Hz Beat frequency 2Hz Waves
Multiple frequencies of different amplitudes added together •complex resultant
Sound waves Resultant tone •Particular musical instrument •Person’s voice Waves
Question Tuning a guitar by comparing sound of the string with that of a standard tuning fork. A beat frequency of 5 Hz is heard when both sounds are present. The guitar string is tighten the and the beat frequency rises to 8Hz. To tune the string exactly to the frequency of the tuning fork what should be done? • a) continue to tighten the string • b) loosen the string • c) it is impossible to determine Resonance Most objects have a natural frequency: Determined by • size • shape •composition System is in resonance if the frequency of the driving force equals the natural frequency of the system
Resonance: examples child being pushed on a swing. Opera singer -breaking glass
Voice Air passages of the mouth, larynx and nasal cavity together form an acoustic resonator.
Voiced sound depend on •resonant frequencies of the total system ------depends on system’s volume and shape Resonance: examples
Tacoma narrows Bridge, WashingtonElectrical State, Resonance: US, 1940Example: Tuning in radio station Adjust resonant frequency of the electrical circuit to the broadcast frequency of the radio station To “pick up” signal Waves Question
Frequency is constant. Its is determined by the source of the wave.
1 Since f Period in constant period
Propagation speed depends on properties of string T vfl mL/