1. Chapter 14: Waves What’s disturbing you?

2. Wave Properties WWWWaves carry energy through matter. TTTThe matter can move with the wave, or at right angles to it. NNNNewton’s laws and conservation laws govern the behavior of waves as well as particles. AAAAll waves transmit energy. Some we see and some we cannot, like sound and light.

3. What are Waves? RRRRhythmic disturbances that carry energy through matter or space are called waves. SSSSome waves require a medium to travel through. These are called Mechanical waves. WWWWater, air, ropes, and springs can “carry” energy through them. MMMMedia can be solids, liquids, or gases. Some are good carriers and some not so good…

4. Two types of waves There are two different fundamental types of waves:  Transverse Waves- the energy moves at right angles to the direction of the medium. Water, light, waves on a rope, electromagnetic waves, most waves move this way Water, light, waves on a rope, electromagnetic waves, most waves move this way  Longitudinal Waves- the energy moves parallel with the direction of the medium. Sound & slinky compressions are the only examples of a longitudinal or compression wave. Most liquids & gases transmit energy this way. Sound & slinky compressions are the only examples of a longitudinal or compression wave. Most liquids & gases transmit energy this way.

5. Identifying Waves

6. Measuring Waves We can describe waves in several aspects:  Speed- Δd/Δt, speed depends on medium  Amplitude- maximum displacement from rest or equilibrium. Greater amplitude is caused by more work, thus more energy (not more speed)  For waves of the same speed, the rate at which energy is transferred is proportional to the square of the amplitude. Double amplitude transfers 4x as much energy/sec.

7. Measuring waves cont’d  Wavelength (λ)- low points are troughs, high points are crests, shortest distance b/t 2 identical points on a wave is one wavelength (m).  Period (T)- the time it takes for a wave to make one complete cycle (oscillation). (s)  Frequency (f)- the number of cycles per second (Hz).

8. Wave Speed Wave Speed  Both period and frequency of a wave depend only on the wave source; not speed or medium.  Wavelength depends on both frequency and wave speed. Speed of a wave is wavelength divided by period, so  Wave speed is frequency times wavelength.

9. Example Problem A sound wave produced by a clock chime is heard 515 m away, 1.5 s later. a. What is the speed of sound of the clock’s chime in air? clock’s chime in air? b. The sound wave has a frequency of 436 Hz. What is its period? 436 Hz. What is its period? c. What is its wavelength?

10. Problem Solved Given: d = 515m, t=1.5s, f=436 Hz v = d / t, T = 1/f a. v = 515m / 1.5s = 343m/s b. T= 1/f = 1/436Hz, T=2.29x10 -3 s c. λ = v / f = (343m/s) / (436Hz) = 0.787m

11. Sonic Boom

12. Sonic Boom Meets Sun Dog

13. Wave Behavior  When a wave reaches a boundary, some of the wave reflects back into the original medium, and some of the wave is transmitted into a new medium.  The amount of reflection or refraction depends on rigidity of the medium.

14. Waves at Boundaries  Remember the speed of a wave through a medium depends on the properties of the medium, not wave amplitude or frequency.  In air, temperature affects speed.  In water, depth affects speed.  In solids, rigidity affects speed.  Waves striking boundaries may be returned to their medium (reflected), or passed through to the next (transmitted).

15. Boundaries cont’d  An incoming wave is called an INCIDENT WAVE.  If an incident wave strikes a barrier and is transmitted, the pulse remains upward.  If an incident wave strikes a barrier and is reflected, the pulse returns to the original medium and can be inverted.  Reflected waves can lose amplitude and transfer energy to the barrier. The wave’s speed does not really decrease.

16. Superposition  Unlike particles of matter, 2 or more waves can exist in the same space at the same time.  The medium will be displaced an algebraic equivalent to the sum of the individual displacements.  This is called interference and can increase (Constructive) or decrease (Destructive) the amplitude of the new wave.

17. Wave Interference  Interference can produce points of zero displacement called nodes.  Points of maximum displacement are called antinodes.  Standing waves appear to stand still due to interference at just the right frequency.

18. Waves in two-dimensions  Ray diagrams help model the movement of waves in 2 dimensions.  A line perpendicular to the barrier is the “normal”  The angle an incident ray makes with the normal will be equal to the angle a reflected ray makes with the normal  This is the law of reflection and holds true for all types of waves.

19. Reflection and Refraction  Waves that return to their medium reflect from a surface following the law of reflection.  Waves that pass through to another medium refract or bend due to a change in speed in the new medium.

20. Diffraction  Waves may bend AROUND a barrier they encounter. Bending around the edges without changing media is called diffraction.  Diffraction also occurs when waves meet a small obstacle. They can bend around it and fill in behind it.