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Waves

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Waves

Overview

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- 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

- Examples

- 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

- 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

- Electromagnetic

- Wave speed is 3 x 108 m/s
- Electric & Magnetic fields are perpendicular

- Electromagnetic type
- Most radio waves are broadcast on 2 bands
- 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?

- AM – amplitude modulation (550-1600 kHz)

- 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

- 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

- 2 types of mechanical waves
- Transverse
- “across”

- Longitudinal
- “along”

- Transverse

- Transverse
- Particles move perpendicularly to the wave motion being displaced from a rest position
- Example – stringed instruments, surface of liquids

- Particles move perpendicularly to the wave motion being displaced from a rest position

>> Direction of wave motion >>

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

>> Direction of wave motion >>

- 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

- Ex. What is the speed of sound at 20°C?

- Vs= 331 + 0.6(T) above 0˚C
- 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)

- Average human ear can detect & process tones from
- 20 Hz (bass – low frequencies) to
- 20,000 Hz (treble – high frequencies)

- What is it?
- The apparent change in frequency of sound due to the motion of the source and/or the observer.

- Moving car example

- Police radar

- 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

THRUST SSC

LSR: 763 mph or 1268 km/hr

- 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.)

- 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?

- 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

Special conditions for amp, freq and λ…

- 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.

- 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…

- 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

- 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

- 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

- Waves occur with antinodes at each end
- fn = nv/2L
- f = frequency
- n = harmonic #
- v = wave speed
- L = length of open pipe

- 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

- 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 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|

f1

f2

|f1-f2|

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

- Simulation lab using EXPLORE
- Standing Waves
- Wave addition