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Module 4.1 – Introduction to Waves

Module 4.1 – Introduction to Waves.

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Module 4.1 – Introduction to Waves

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  1. Module 4.1 – Introduction to Waves Waves are caused by vibrations, such as objects undergoing simple harmonic motion. Although water waves, sound waves, springs, and light all seem very different, they share many properties that can be explained using a wave model. This module introduces trainees to some general wave properties which will later be applied to specific types of waves.

  2. Period and Frequency • Period – time it takes for one complete cycle • Frequency – number of cycles per unit time

  3. Example A child swings back and forth on a swing 15 times in 30.0 s. Determine the frequency and period of the swing.

  4. Wave Terminology • Wave – a disturbance that transfers energy

  5. Mechanical Waves • Transverse Wave • Longitudinal Wave

  6. Wave Terminology

  7. 1D Wave Properties Wave Simulator • Wave speed depends only on the medium Upright reflected wave Light Medium Heavy medium Inverted reflected wave Light medium Heavy Medium

  8. Superposition • When waves collide they simply pass through one another unchanged. They continue on as if there were no interaction. • While the waves overlap, they temporarily produce a resultant wave due to interference. The displacement of the medium is the sum of the displacements of each component wave • Constructive Interference • Destructive Interference

  9. Superposition Constructive Interference Destructive Interference Node

  10. Resonance and Standing Waves • Resonance – achieved when energy is added to a system at the same frequency as its natural frequency; • Results in maximum amplitude. • Standing Wave – example of resonance

  11. Check Your Learning • The ? of a wave depends only on the medium in which it is travelling. • Frequency • Period • Speed • Wavelength (c) speed • When a wave passes from one medium to another, the ? must stay the same. • Amplitude • Frequency • Speed • Wavelength (b) frequency

  12. Check Your Learning • A wave in which the medium moves parallel to the medium is called a ? wave. • Electromagnetic • Longitudinal • Mechanical • Transverse (b) longitudinal • The vertical distance from the top of a crest to the bottom of a trough is 34.0 cm. The amplitude of this wave is • 8.5 cm • 17.0 cm • 34.0 cm • 68.0 cm (b) 17.0 cm

  13. Check Your Learning • A pulse goes into a medium that is less dense. The reflected pulse is • Faster • Inverted • Larger • Upright (d) upright • Resonance occurs when one object causes a second object to vibrate. The second object must have the same natural • Amplitude • Frequency • Speed • Wavelength (b) frequency

  14. Check Your Learning • A wave source has a period of 0.20 s. What is the frequency? • 0.20 Hz • 1.0 Hz • 5.0 Hz • 20. Hz (c) 5.0 Hz

  15. Wave Equation • Wave velocity – the velocity at which the wave crests (or any other part of the wave) move; • not the same as the velocity of a particle of the medium.

  16. Example 1 A hiker shouts toward a vertical cliff 685 m away. The echo is heard 4.00 s later. The wavelength of the sound is 0.750 m. • What is the speed of sound in air? • What is the frequency? • What is the period of the wave?

  17. Solution

  18. Example 2 Water waves have a wavelength of 3.2 m and a frequency of 0.78 Hz. • At what rate does a stationary boat bob up and down? • If the boat starts moving into the waves (in the opposite direction to) at a speed of 5.0 m/s, at what rate will the boat bob up and down now?

  19. Solution • Since the boat is not moving, it will bob up and down at the same frequency as the waves.

  20. Check Your Learning Water waves in a lake travel 4.4 m in 1.8 s. The period of oscillation is 1.2 s. What is the speed and wavelength of the water waves?

  21. Reflection Law of Reflection

  22. Refraction • Refraction – change in speed while going from one medium to another results in a change of direction of the wave

  23. Refraction

  24. Diffraction • Diffraction – waves bend around the edges of the barrier

  25. Diffraction

  26. Interference

  27. Check Your Learning • The direction a wave moves is • Parallel to the wavefronts. • Perpendicular to the wavefronts. • In the direction of increasing density. • In the direction of increasing wavelength. (b) Perpendicular to the wavefronts. • The process by which a wave bounces off an obstacle in its path is called • Diffraction • Reflection • Refraction • Superposition (b) Reflection

  28. Check Your Learning • The bending of waves as they go through a small opening is called • Diffraction • Reflection • Refraction • Superposition (a) Diffraction • The bending of waves as they go from one medium to a new medium is called • Diffraction • Reflection • Refraction • Superposition (c) Refraction

  29. Check Your Learning • When two waves interfere with one another, the word interfere means • One wave prevents the other wave from finishing its cycle. • One wave stops moving while the other passes. • The motion we observe is the sum of the motions of the two individual waves. • The wave with the larger amplitude grows and the wave with the smaller amplitude shrinks. (c) The motion we observe is the sum of the motions of the two individual waves.

  30. Module Summary In this module you have learned that • Mechanical waves need a medium while electromagnetic ones do not. • Mechanical waves can be transverse or longitudinal. • The correct terminology to use when describing waves, such as: period, frequency, crest, trough, amplitude, wavelength • The speed of a wave depends only upon the medium in which it is travelling. • Waves will be both reflected and transmitted at a boundary.

  31. Module Summary • The frequency of a wave does not change when going from one medium to another one. • When waves interfere with one another, they can interfere constructively or destructively before passing through one another unchanged. • A standing wave is an example of resonance in a medium. • All waves are governed by the wave equation

  32. Module Summary • All two-dimensional waves obey the law of reflection, which states that the angle of incidence is equal to the angle of reflection • All two-dimensional waves undergo refraction, diffraction, and interference.

  33. Module 4.2 – Sound Waves In this module, the wave properties studied in module 7.2 will be looked at in greater depth as they apply to sound waves. Although these properties can be observed in general with all waves, they are often easily observable and can be demonstrated using these specific types of waves. Sound waves are used in a variety of techniques in exploring for oil and minerals.

  34. Sound Waves • Mechanical Wave (longitudinal) • Series of compressions and rarefactions

  35. Sound Properties

  36. Range of Hearing • Human Hearing infrasonic ultrasonic 20 Hz 20000 Hz • Range decreases as we age • Many animals can hear above our range of hearing

  37. Speed of Sound • Mechanical waves need a medium • Medium determines speed of sound

  38. Speed of Sound in Air Mach Number Supersonic – Mach Number is greater than one

  39. Example A plane is flying at a speed of 855 m/s. If the air temperature is 12oC, • What is the speed of sound? • What is the Mach number for the plane?

  40. Solution

  41. Doppler Effect Observer A hears a higher frequency

  42. Sonic Boom

  43. Check Your Learning • Which of the following is NOT a property of sound? • Amplitude • Frequency • Mass • Wavelength (c) Mass • The average human ear cannot hear frequencies above • 20 Hz • 2000 Hz • 20000 Hz • 200000Hz (c) 20000 Hz

  44. Check Your Learning • When we describe something as supersonic we mean it is • Faster than the speed of sound • Higher in frequency than 20000 Hz • Lower in frequency than 20 Hz • Slower than the speed of sound (a) Faster than the speed of sound • When the amplitude of a sound wave increases, • The wavelength of the sound decreases • The sound gets louder • The pitch increases • The speed of sound increases (b) The sound gets louder

  45. Check Your Learning • Sound is a longitudinal wave because • The oscillations in pressure are in the same direction as the wave moves. • The oscillations in pressure are perpendicular to the direction that the wave moves. • The wavelength is long compared to light waves. • The wavelength is always longer than the amplitude. (a) The oscillations in pressure are in the same direction as the wave moves.  • The wavelength of a sound wave can be calculated by • Multiplying the amplitude by the frequency • Dividing the amplitude by the frequency • Multiplying the speed by the frequency • Dividing the speed by the frequency (d) Dividing the speed by the frequency (the wave equation)

  46. Check Your Learning • The speed of sound in air at 7.0oC is • 331 m/s • 332 m/s • 335 m/s • 338 m/s (c) 335 m/s (using v=331+0.59T) • A person is behind an ambulance as it moves away from her. The pitch of the sound that she hears is • Lower than if the ambulance was stationary. • The same as if the ambulance was stationary. • Higher than if the ambulance was stationary. (a) Lower than if the ambulance was stationary, since the wavelength will be larger behind the ambulance.

  47. Closed Air Columns • Standing wave in a closed air column requires a node at the closed end and an antinode at the open end of the air column Full Standing Wave

  48. Resonant Lengths

  49. Example 1 Calculate the first 3 resonant lengths for a 512 Hz tuning fork, assuming that the air temperature is 20.0oC.

  50. Solution

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