Waves and Sound

1. Waves and Sound

2. Work • To move an object we must do work • Work is calculated as the force applied to the object through a distance or: • Work has the units Newton meters (N m) or Joules • 1 Joule = 1 N m

3. Energy • There are 2 types of Energy that we will deal with, Kinetic energy and Potential Energy • Potential Energy: is the energy of position or stored energy • Ep = (Δd) • Kinetic Energy: is the energy of motion • Ek = ½ mv2

4. What amount of work is done by Jane as she lifts a box of mass 20.0 kg to a height of 1.5 m? W = (x) W = (20.0 kg)(9.81 m/s2)(1.5 m) W = 294 J What is the Kinetic energy of an object moving at 5.00 m/s that has a mass of 5.00 kg? Ek = ½ mv2 Ek = ½(5.00 kg)(5.00 m/s)2 Ek = 62.5 J Work and Energy Examples

5. Waves

6. What are Waves?? • They are the motion of a disturbance. • They are a means of transferring energy without the particle moving.

7. Classifications of Waves

8. Simple Harmonic Motion

9. Periodic Motion • Motion that repeats itself over and over • Ex: heart beats, ticking clock, moving on a swing • The time it takes for one complete cycle of the motion is called the ……. Period

10. Other Terms to Know • Cycle – One complete back and forth motion • Frequency – the number of cycles per unit time. It is measured in Hertz (Hz) • Displacement – the distance an object moves from the equilibrium position • Amplitude – the maximum displacement

11. Simple Harmonic Motion (SHM) • A type of periodic motion • Objects that vibrate with SHM are called Simple Harmonic Oscillators • An example of this is a mass on a spring, pendulums, and waves

12. Mass on a spring • When there is a mass on a spring, there are 2 forces that are acting on it. • Gravity and the Tension of the spring • Tension on the spring is governed by Hooke’s Law

13. Hooke’s Law F is Force k is the spring constant X is the displacement • When the spring is stretched FT > Fg then the mass moves upwards • When the spring is compressed Fg > FT then the mass moves downwards

14. Hooke’s Law Example • A mass of 15.0 kg is suspended from a spring. If the spring has a spring constant is 6.00 N/m, what is the restoring force of the spring when the mass is 0.30 m from equilibrium? -(6.00 N/m)(0.30 m) -1.8 N

15. MASS ON A SPRING e M A Stretch & Release k = the spring constant in N m-1

16. Mass on a Spring Example • A 0.23 kg object vibrates at the end of a horizontal spring (k = 32 N/m) along a frictionless surface. What is the period of the vibration? T = 2p√(m/k) T = 2p√(0.23 kg / 32 N/m) T = 0.53 s

17. Hooke’s Law Cont. • If there was no force to slow the motion down, it would continue forever • The force that causes the slowing of the motion is called the Restoring Force • The Restoring force is governed by the spring constant, k

18. INITIAL AMPLITUDE time DAMPING DISPLACEMENT THE AMPLITUDE DECAYS EXPONENTIALLY WITH TIME

19. Hooke’s Law Cont. • When there is a Restoring force, the systems will become damped • Where is this idea of a damped system used in your daily life???

20. l THE PENDULUM The period, T, is the time for one complete cycle.

21. Pendulum Example • Find the length of a pendulum that has a period of 0.90 s. T = 2p√(l/g) 0.90 s = 2p√(l / 9.81 m/s2) l = (0.90 s / 2p)2(9.81 m/s2) l = 0.20 m

22. Energy in SHM • Work is done on an object when we apply a force over a distance • For a spring, the work is moving the object to its maximum displacement

23. Potential Energy stored in the spring is Ep = ½ x And k x So Ep = ½ k x2 But the mass moves on the spring back and forth changing from Kinetic to potential Energy Kinetic Energy is: Ek = ½ mv2 Total Mechanical Energy is: ET = Ep + Ek ET = ½ k x2 + ½ mv2 Energy in SHM Cont.

24. Are there different Types of Waves?? You bet there are

25. Types of Waves • Longitudinal • Transverse • Surface

26. Transverse waves • The wave particles vibrate perpendicular to the transfer of energy • An example of this is a wave on a string • Waves in solids are transverse waves

27. Transverse waves • Crests Highest part of a wave • Troughs The low points of the wave

28. Longitudinal Waves • The wave particles vibrate parallel to the transfer of energy • An example of this is a sound wave • Waves in gases and liquids usually are longitudinal waves

29. Compressions The close together part of the wave • Rarefactions The spread-out parts of a wave

30. What the waves look like

31. Surface Waves • These are waves that move particles in both longitudinally and transversely • Ex: Water waves

32. Wave Characteristics

33. Wave Characteristics • All waves have 5 Characteristics • Frequency • Period • Wavelength • Velocity • Amplitude

34. Wave Characteristics Cont. • Frequency (f) • the number of cycles or oscillations per second. • Measured as 1/s, or s-1, or Hertz (Hz) • 1 Hz = 1 cycle per second • Ex: A car travels 8 times around a track in 4 seconds. What is the frequency? • f = #cycles/time = 8/4 = 2 Hz

35. Wave Characteristics Cont. • Period (T) • The time required for one cycle to be completed • Measured in seconds (s) • T = 1/f • Ex: What is the period from the previous question? • T = 1/f = ½ = 0.5 s

36. Wave Characteristics Cont. • Wavelength (l) • The distance between successive parts of a wave. • The parts can be either the Crest or the Trough of the wave

37. Wave Characteristics Cont. • Velocity (v) • The speed of a wave through a medium depends on the Elasticity and the density of the medium • V = √(elasticity/density) • The speed of the wave can also be determined using the wave characteristics • v = l/ T or v = lf • Which is known as the Universal Wave Equation • Which is a form of uniform motion: v = Δd/Δt

38. Velocity Example • Ex: What is the velocity of a wave with a frequency of 10 Hz and a wavelength of 10 m? • v = lf • v = 10 Hz * 10 m • v = 100 m/s

39. Wave Characteristics Cont. • Amplitude (x) • The maximum displacement from equilibrium (or rest position) of a wave

40. Wave Characteristics

41. Propagation Reflection Polarization Refraction Diffraction Interference Diffusion Color Dispersion Scattering 10 Characteristics of Waves

42. 1-Dimensional Waves

43. Propagation • How a wave moves from one position to another • All the motion is in a straight line • Wave speed is determined by the medium that it is traveling in • Calculated using either • v = Δd/Δt • v = fλ

44. Reflection • The bouncing of a wave off a reflective boundary • Law of Reflection • Θi = Θreflection • v, f, T, and λ DO NOT CHANGE

45. Polarization • When the displacement of the particles is in the same plane • Passing a wave through a slit aligned in a direction produces a polarized wave • If 2 slits that are perpendicular are used, the wave is destroyed • Does not occur in Longitudinal waves only Transverse waves

46. Refraction • Occurs when a wave meets a boundary at an angle • Where the wave and the boundary meet, the angle taken from the normal is called the Angle of Incidence Θi

47. Refraction Cont. • v and λ must change because you are going into a new medium • The speed will decrease when the wave refracts to the normal • The speed will increase when the wave refracts away from the normal • To calculate the angles, speed, and wavelengths λ1 =sin Θ1 =v1=n2 λ2 sin Θ2 v2 n1

48. Refraction Cont. • n refers to the Index of Refraction and is an indication of the density in comparison to the density of air • i refers to the incident medium and r to the refractive medium • In this form, the equations are only to be used with mechanical waves

49. Refraction Example • Waves travel from deep water into shallow water. If the angle of incidence is 30.0o, and the angle of refraction is 20.0o, what is the index of refraction? • sinΘ1 = n sinΘ2 sin 30.0o = n n = 1.46 sin 20.0o

50. Diffraction • Are waves able to bend around corners? • Yes they can, this is called Diffraction • How much they bend depends on the wavelength and the size of the opening • ↑ the λ the ↑ the diffraction and vice versa • ↓ the opening the ↑ the diffraction