Waves

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Waves. Overview (Text p382&gt;). Waves – What are they?. Imagine dropping a stone into a still pond and watching the result. A wave is a disturbance that transfers energy from one point to another in wave fronts. Examples Ocean wave Sound wave Light wave Radio wave .

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Presentation Transcript

Waves

Overview

(Text p382>)

Waves – What are they?
• Imagine dropping a stone into a still pond and watching the result.
• A wave is a disturbance that transfers energy from one point to another in wave fronts.
• Examples
• Ocean wave
• Sound wave
• Light wave
Waves – Basic Characteristics
• Frequency (f) cycles/sec (Hz)
• Period (T) seconds
• Speed (v) meters/sec
• Amplitude (A) meters
• Wavelength () meters
• Peak/Trough
• Wave spd = w/length * freq
• v =  * f
Wave Types
• 2 types of waves:
• Electromagnetic
• Require NO medium for transport
• Speed is speed of light @ 3 x 108 m/s
• Examples – light, radio, heat, gamma
• Mechanical
• Require a medium for transport of energy
• Speed depends on medium material
• Examples – sound, water, seismic
Waves – Electromagnetic
• Wave speed is 3 x 108 m/s
• Electric & Magnetic fields are perpendicular
• Electromagnetic type
• AM – amplitude modulation (550-1600 kHz)
• Ex. WTON 1240 kHz
• FM – frequency modulation (86 – 108 MHz)
• Ex. WMRA 90.7 MHz
• What are their respective wavelengths?
Practice
• What is the wavelength of the radio carrier signal being transmitted by WTON @1240 kHz?
• Solve c = λ*f for λ.
• 3e8 = λ * 1240e3
• λ = 3e8/1240e3 = 241.9 m
Practice
• What is the wavelength of the radio carrier signal being transmitted by WMRA @ 90.7 MHz?
• Solve c = λ*f for λ.
• 3e8 = λ * 90.7e6
• λ = 3e8/90.8e6 = 3.3 m
Mechanical Waves
• 2 types of mechanical waves
• Transverse
• “across”
• Longitudinal
• “along”
Waves – Mechanical Transverse
• Transverse
• Particles move perpendicularly to the wave motion being displaced from a rest position
• Example – stringed instruments, surface of liquids

>> Direction of wave motion >>

Waves - Mechanical Longitudinal
• Particles move parallel to the wave motion, causing points of compression and rarefaction
• Example - sound

>> Direction of wave motion >>

Sound
• Speed of sound in air depends on temperature
• Vs= 331 + 0.6(T) above 0˚C
• Ex. What is the speed of sound at 20°C?
• Ss = 331 + 0.6 x 20 = 343 m/s
• Speed of sound also depends upon the medium’s density & elasticity. In materials with high elasticity (ex. steel 5130 m/s) the molecules respond quickly to each other’s motions, transmitting energy with little loss.
• Other examples – water (1500), lead (1320) hydrogen (1290)

Speed of sound = 340 m/s (unless other info is given)

Sounds and humans
• Average human ear can detect & process tones from
• 20 Hz (bass – low frequencies) to
• 20,000 Hz (treble – high frequencies)
Doppler Effect
• What is it?
• The apparent change in frequency of sound due to the motion of the source and/or the observer.
Doppler Effect
• Moving car example
Doppler Effect Formula
• f’ = apparent freq
• f = actual freq
• v = speed of sound
• vo = speed of observer (+/- if observer moves to/away from source)
• vs = speed of source (+/- if source moves to/away from the observer)
• Video example
Sound Barrier #2

THRUST SSC

LSR: 763 mph or 1268 km/hr

Doppler Practice
• A police car drives at 30 m/s toward the scene of a crime, with its siren blaring at a frequency of 2000 Hz.
• At what frequency do people hear the siren as it approaches?
• At what frequency do they hear it as it passes? (The speed of sound in the air is 340 m/s.)
Doppler Practice
• A car moving at 20 m/s with its horn blowing (f = 1200 Hz) is chasing another car going 15 m/s.
• What is the apparent frequency of the horn as heard by the driver being chased?
Interference of Waves
• 2 waves traveling in opposite directions in the same medium interfere.
• Interference can be:
• Constructive (waves reinforce – amplitudes add in resulting wave)
• Destructive (waves cancel – amplitudes subtract in resulting wave)
• Termed - Superposition of Waves
Superposition of Waves

Special conditions for amp, freq and λ…

Standing Wave?
• A wave that results from the interference of 2 waves with the same frequency, wavelength and amplitude, traveling in the opposite direction along a medium.
• There are alternate regions of destructive (node) and constructive (antinode) interference.
Basic Terms
• Harmonic number
• n (1st, 2nd, 3rd, …)
• Fundamental frequency
• f1(n=1, 1st harmonic)
• Nth harmonic frequency
• fn = n * f1
• Length of string/pipe
• L
• Wave speed
• v = 340 m/s in pipes

2 models for discussion…

Standing Waves in Strings
• Nodes occur at each end of the string
• Harmonic # = # of envelopes
• fn = nv/2L
• f = frequency
• n = harmonic #
• v = wave velocity
• L = length of string
Practice
• An orchestra tunes up by playing an A with fundamental frequency of 440 Hz.
• What are the second and third harmonics of this note?
• Solve fn = n*f1
• f1 = 440
• f2 = 2 * 440 = 880 Hz
• f3 = 3 * 440 = 1320 Hz
String Practice
• A C note is struck on a guitar string, vibrating with a frequency of 261 Hz, causing the wave to travel down the string with a speed of 400 m/s.
• What is the length of the guitar string?
• Solve fn = nv/(2L) for L
• L = nv/(2f)
• L = 0.766 m
Standing Waves in Open Pipes
• Waves occur with antinodes at each end
• fn = nv/2L
• f = frequency
• n = harmonic #
• v = wave speed
• L = length of open pipe
Standing Waves in Pipes (closed at one end)
• Waves occur with a node at the closed end and an antinode at the open end
• Only odd harmonics occur
• fn = nv/4L
• f = frequency
• n = harmonic #
• v = wave speed
• L = length of pipe
Pipe Practice
• What are the first 3 harmonics in a 2.45 m long pipe that is:
• Open at both ends
• Closed at one end
• Solve
• (open) fn = nv/(2L) find f1, f2, f3
• (closed @ 1 end) fn = nv/(4L) find f1, f3, f5
Beats
• Beats occur when 2 close frequencies (f1, f2) interfere
• Reinforcementvscancellation
• Pulsating tone is heard
• Frequency of this tone is the beat frequency (fb)
• fb = |f1 - f2|
Beats

f1

f2

|f1-f2|

Ex. If f1 = 440 Hz and f2 = 420 Hz, then fb = (440-420) = 20 Hz

Lab Practice
• Simulation lab using EXPLORE
• Standing Waves