Waves – Topic 4 Chapters 13, 14, 25, 26

Traveling Waves  Wave Motion: Disturbance which travels in a medium transferring energy and momentum. –No Transfer of Mass!!!  Two Classifications –Mechanical Waves (require a medium)  Ex: sound, water, Earth Quakes –Electromagnetic Waves (travel in vacuum)  Ex: light, microwaves – see chart

Speed depends on Medium  Sound depends on Temp & Pressure  Strings/Springs depends on tension and linear mass density  Electromagnetic waves all travel the same speed in a vacuum. 3.0 x 10 8 m/s.

Speed depends on Medium  Velocity of sound at STP is 330 m/s. (Standard Pressure and Temp.) STP - 1 atmosphere and 0˚Celsius.  +/- 0.6 m/s for every 1˚C +/-  At room temp. (22 degrees) v ≈ 343 m/s

Table 14-1 Speed of Sound in Various Materials Aluminum6420 Granite6000 Steel5960 Pyrex glass 5640 Copper5010 Plastic2680 Fresh water (20 ºC) 1482 Fresh water (0 ºC) 1402 Hydrogen (0 ºC) 1284 Helium (0 ºC) 965 Air (20 ºC) 343 Air (0 ºC) 331 Material Speed (m/s)

Reflection of Pulses  The pulse becomes inverted upon reflecting off the fixed end.

Reflection at boundary  The transmitted pulse is not inverted and maintains the same phase. The reflected pulse is is also not inverted.

Sound is Longitudinal Wave Displacement of the particle is parallel to the propagation or direction of wave travel.

Light is Transverse Wave Displacement of the particle is at right angles to the propagation or direction of wave travel.

Conceptual Checkpoint 14-2 How far away is the lightning?

Echo Problem  You shout at a canyon wall and here your echo 2.4 seconds after you shout. How far away is the canyon wall? Assume v = 343 m/s  d = vt  d= 343m/s (1.2 sec) half the time  d= 412 m to the wall.

Wishing Well – Making a Splash!  How long after dropping the stone will the boy hear the splash?

Making a Splash - Solution  First calculate the time for the stone to reach the water. d=v i t + ½gt 2  t= 1.22 sec  Then calculate the time for the sound wave to travel back up. d=vt  t= 0.02 sec  Add the two times. t= 1.24 sec

PeriodicPeriodic Waves - Terminology Waves PeriodicWaves  Frequency – The number of vibrations or oscillations per unit time. Unit Hertz (Hz) – derived.  Period – Time required for one complete cycle or to move the linear distance of one wavelength. Unit second (s) – Fundamental.  Amplitude – The maximum displacement of a particle of the medium from the rest position. Unit meter (m)– Fundamental.  Wavelength – The distance traveled by one wave in one period. The distance between two consecutive points in phase. Unit Meter (m) – Fundamental.

Traveling Wave Characteristics  Frequency is the reciprocal of Period f = 1/T or T = 1/f  Determine the frequency of a wave with a period of sec.  f =1/T, f = 1/ ( sec) = 60 Hz  What happens to the period of a wave as its frequency increases?

Wave Speed – wave equation  Wave equation can be derived from the kinematics equation v = d/t  If d=λ(wavelength) and t=T(period), then v= λ/T  Since f = 1/T, then  v = f λ

Wave Speed  A sound wave in a steel rail has a frequency of 620 Hz and a wavelength of 10.5 m. what is the speed of sound in steel?  v=f λ  v= 620hz (10.5 m)  v= 6510 m/s

Periodic Wave Phenomena  Huygens Principle: - Wavelets! Huygens Principle Huygens Principle –This principle uses the wave concepts to explain periodic wave phenomena.  Reflection  Refraction  Diffraction  Wave-fronts Wave-fronts  Sun Ripple Sun Ripple Sun Ripple

Reflection  Law of Reflection –The angle of incidence equals the angle of reflection. Θ i = θ r  The incident and reflected rays lie in the same plane with the normal.

Refraction  Sudden change in direction of a wave as it changes speed. –It must enter obliquely to change direction!

Refraction  In both cases the speed of the wave has decreased. This is indicated by the decrease in wavelength!

Refraction of Sound Refraction of Sound  When a wave slows down it bends closer to the normal.  When a wave speed up it bends away from the normal.

Diffraction  The bending or spreading out around the edges of a barrier or obstruction.  Does the speed change?  No! You can see the wavelength is constant.

Diffraction  The extent of the diffraction depends on the ratio of the wavelength to the opening of the hole.  The extent of the diffraction depends on the ratio of the wavelength to the opening of the hole.  Diffraction ~ λ/D Diffraction ~ λ/D Diffraction ~ λ/D  Tsunami Waves Tsunami Waves Tsunami Waves

Interference Constructive Interference Destructive Interference Waves DO NOT bounce! Energy passes through.

Superposition  The Algebraic sum of the amplitudes of two or more waves which form interference. interference  Waves which arrive in phase form constructive interference.  Waves which meet out of phase form destructive interference.

Standing or Stationary Waves Stationary WavesStationary Waves  Conditions need: –Same Amplitude –Same frequency –Opposite Directions  Caused by both Constructive and Destructive interference. –Nodes – Destructive –Antinodes - Constructive

Harmonics  Vibrating strings or pipes form Stationary wave patterns each pattern refers to a different Harmonic.

Beats  When two frequencies are very close they interfere creating a beat sound.  Beat frequency = F1 –F2

Figure Interference with Two Sources

Interference Path Diff = n λ, Constructive Int.

Doppler Effect Doppler Effect  E E E E E O O O O O O O  Movement toward or decreasing distance produced a higher frequency.

Figure The Doppler Effect: A Moving Observer

Doppler Effect What happens when the moving source reaches or exceeds the speed of the wave? The Doppler Effect and Sonic Booms Plane-Mach1

Resonance  Is it Live or is it Memorex –viewed under a strobe light Is it Live or is it Memorex Is it Live or is it Memorex  An Incredibly Irritating Resonance Demonstration An Incredibly Irritating Resonance Demonstration An Incredibly Irritating Resonance Demonstration  Resonating Wave – Match the λ Resonating Wave – Match the λ Resonating Wave – Match the λ

Tacoma Narrows Bridge Tacoma Narrows Bridge  On November 7, 1940, at approximately 11:00 AM, the first Tacoma Narrows suspension bridge collapsed due to wind- induced vibrations.  On November 7, 1940, at approximately 11:00 AM, the first Tacoma Narrows suspension bridge collapsed due to wind- induced vibrations.  Situated on the Tacoma Narrows in Puget Sound, near the city of Tacoma, Washington, the bridge had only been open for traffic a few months.