Waves. Overview (Text p382>)

Transcription

1 Waves Overview (Text p382>)

2 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

3 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

4 Wave Basic Structure

5 Wave Types 2 types of waves: Electromagnetic Require NO medium for transport Speed is speed of 3 x 10 8 m/s Examples light, radio, heat, gamma Mechanical Require a medium for transport of energy Speed depends on medium material Examples sound, water, seismic

6 Waves Electromagnetic Wave speed is 3 x 10 8 m/s Electric & Magnetic fields are perpendicular

7 Waves Radio Electromagnetic type Most radio waves are broadcast on 2 bands AM amplitude modulation ( khz) Ex. WTON 1240 khz FM frequency modulation ( MHz) Ex. WMRA 90.7 MHz What are their respective wavelengths?

8 Practice What is the wavelength of the radio carrier signal being transmitted by khz? Solve c = λ*f for λ. 3e8 = λ * 1240e3 λ = 3e8/1240e3 = m

9 Practice What is the wavelength of the radio carrier signal being transmitted by 90.7 MHz? Solve c = λ*f for λ. 3e8 = λ * 90.7e6 λ = 3e8/90.8e6 = 3.3 m

10 Mechanical Waves 2 types of mechanical waves Transverse across Longitudinal along

11 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 >>

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

13 Longitudinal Waves

14 Sound Speed of sound in air depends on temperature S s = (T) above 0 C Ex. What is the speed of sound at 20 C? S s = 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)

15 Sounds and humans Average human ear can detect & process tones from 20 Hz (bass low frequencies) to 20,000 Hz (treble high frequencies)

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

17 Doppler Effect Moving car example

18 Doppler Effect Example Police radar

19 Doppler Effect Formula f = apparent freq f = actual freq v = speed of sound v o = speed of observer (+/- if observer moves to/away from source) v s = speed of source (+/- if source moves to/away from the observer) Video example f' f v v v v o s

20 Sound Barrier #1

21 Sound Barrier #2

22 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.)

23 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?

24 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

25 Superposition of Waves

26 Superposition of Waves Special conditions for amp, freq and λ

27 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.

28 Standing Wave 2 models for discussion

29 Standing Waves in Strings Nodes occur at each end of the string Harmonic # = # of envelopes f n = nv/2l f = frequency n = harmonic # v = wave velocity L = length of string

30 Standing Waves in Strings

31 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 f n = n*f 1 f 1 = 440 f 2 = 2 * 440 = 880 Hz

32 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 f = nv/(2l) for L L = nv/(2f) L = m

33 Standing Waves in Open Pipes Waves occur with antinodes at each end f n = nv/2l f = frequency n = harmonic # v = wave speed L = length of open pipe

34 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 f n = nv/4l f = frequency n = harmonic # L = length of pipe

35 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) f n = nv/(2l) 1 end) f n = nv/(4l)

36 Beats Beats occur when 2 close frequencies (f 1, f 2 ) interfere Reinforcement vs cancellation Pulsating tone is heard Frequency of this tone is the beat frequency (f b ) f b = f 1 - f 2

37 Beats f 1 f 2 f 1- f 2