Waves in One Dimension


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Waves in One Dimension

  1. 1. Physics 30S Unit 1 - Waves
  2. 2. Physics 30S Unit 1 - Waves
  3. 3. Unit 1 - Waves <ul><li>We begin our study of physics with a study of waves in one dimension. There are many examples in nature and in the human use of waves such as ocean waves, sound waves, vibrations produced by musical instruments, and the many applications of electromagnetic waves in the communications industry. </li></ul>Waves in One Dimension
  4. 4. Unit 1 - Waves <ul><li>A mechanical wave can be described as a disturbance, a transfer of energy, which travels through a medium from one location to another location. </li></ul><ul><li>A single disturbance moving through a medium from one location to another location is described as a pulse . </li></ul><ul><li>A repeating disturbance moving over some prolonged period of time through a medium from one location to another is referred to as a periodic wave . </li></ul>What is a wave?
  5. 5. Unit 1 - Waves <ul><li>A medium is a substance or material which carries the disturbance (either a pulse, wave or periodic wave) from one location to another. The wave medium is not the wave and it doesn't make the wave; it merely carries or transports the wave from its source to other locations. </li></ul>What is a wave?
  6. 6. Unit 1 - Waves <ul><li>To fully understand the nature of a wave, it is important to consider the medium as a series of interconnected or merely interacting particles. In other words, the medium is composed of parts which are capable of interacting with each other. The interactions of one particle of the medium with the next adjacent particle allows the disturbance to travel through the medium. </li></ul><ul><li>When a wave is present in a medium (that is, when there is a disturbance moving through a medium), the individual particles of the medium are only temporarily displaced from their rest position. There is always a force acting upon the particles which restores them to their original position. It is for this reason, that a wave is said to involve the movement of a disturbance without the movement of matter. </li></ul>What is a wave?
  7. 7. Unit 1 - Waves <ul><li>Waves are said to be an energy transport phenomenon. As a disturbance moves through a medium from one particle to its adjacent particle, energy is being transported from one end of the medium to the other. </li></ul><ul><li>This characteristic of a wave as an energy transport phenomenon distinguishes waves from other types of phenomenon. In a wave phenomenon, energy can move from one location to another, yet matter does not move. A wave transports its energy without transporting matter. </li></ul>What is a wave?
  8. 8. Unit 1 - Waves <ul><li>A wave can be described as a disturbance which travels through a medium, transporting energy from one location (its source) to another location without transporting matter. Each individual particle of the medium is temporarily displaced and then returns to its original equilibrium positioned . </li></ul>Conclusion
  9. 9. Nature of Waves
  10. 10. Unit 1 - Waves <ul><li>A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction which the wave moves. Transverse waves are always characterized by particle motion being perpendicular to wave motion. </li></ul>Transverse Waves
  11. 11. Unit 1 - Waves <ul><li>A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. Longitudinal waves are always characterized by particle motion being parallel to wave motion. </li></ul>Longitudinal Waves
  12. 12. Unit 1 - Waves <ul><li>A surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse. In longitudinal and transverse waves, all the particles in the entire bulk of the medium move in a parallel and a perpendicular direction (respectively) relative to the direction of energy transport. In a surface wave, it is only the particles at the surface of the medium which undergo the circular motion. The motion of particles tend to decrease as one proceeds further from the surface. </li></ul>Surface Waves
  13. 13. Unit 1 - Waves Longitudinal Waves Transverse Waves Surface Waves
  14. 14. Unit 1 - Waves Transverse Waves & Longitudinal Waves Simulation Activity
  15. 15. Unit 1 - Waves Anatomy of a Wave
  16. 16. Unit 1 - Waves <ul><li>The frequency (f) of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. Given this definition, it is reasonable that the quantity frequency would have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. </li></ul>Frequency & Period of a Wave
  17. 17. Unit 1 - Waves <ul><li>Period (T) refers to the time which it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. </li></ul>Frequency & Period of a Wave
  18. 18. Unit 1 - Waves <ul><li>Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens; period refers to the time it takes something to happen. Frequency is a rate quantity; period is a time quantity. Frequency is the cycles/second; period is the seconds/cycle. </li></ul>Frequency & Period of a Wave
  19. 19. Unit 1 - Waves <ul><li>Mathematically, the period is the reciprocal of the frequency and vice versa. In equation form, this is expressed as follows. </li></ul><ul><li>Since the symbol f is used for frequency and the symbol T is used for period, these equations are also expressed as: </li></ul>Frequency & Period of a Wave
  20. 20. Unit 1 - Waves Frequency & Period of a Wave
  21. 21. Unit 1 - Waves <ul><li>The velocity of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. In the case of a wave, the velocity is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. In equation form, </li></ul><ul><li>velocity = distance/time </li></ul>The Velocity of a Wave
  22. 22. Unit 1 - Waves <ul><li>If the crest of an ocean wave moves a distance of 20 meters in 5 seconds, then the velocity of the ocean wave is 4 m/s. On the other hand, if the crest of an ocean wave moves a distance of 25 meters in 5 seconds (the same amount of time), then the velocity of this ocean wave is 5 m/s. The faster wave travels a greater distance in the same amount of time. </li></ul>The Velocity of a Wave
  23. 23. Unit 1 - Waves <ul><li>A wave is produced when a vibrating source displaces the first particle of a medium. The frequency at which each individual particle vibrates is equal to the frequency at which the source vibrates. Similarly, the period of vibration of each individual particle in the medium is equal to the period of vibration of the source. In one period, the source is able to displace the first particle upwards from rest, back to rest, downwards from rest, and finally back to rest. This complete back-and-forth movement constitutes one complete wave cycle. </li></ul>The Wave Equation
  24. 24. Unit 1 - Waves <ul><li>The motion of the disturbance along the medium after every one-fourth of a period is depicted. Observe the hand has made one complete back-and-forth motion. A period has elapsed. Observe that during this same amount of time, the disturbance has moved a distance equal to one complete wavelength. So in a time of one period, the wave has moved a distance of one wavelength. </li></ul>The Wave Equation
  25. 25. Unit 1 - Waves <ul><li>Combining this information with the equation for velocity (v =  d/t), it can be said that the velocity of a wave is also the wavelength/period. </li></ul><ul><li>velocity = wavelength/period </li></ul><ul><li>v =  /T </li></ul><ul><li>Since the period is the reciprocal of the frequency, the expression 1/f can be substituted into the above equation for period. Rearranging the equation yields a new equation of the form: </li></ul><ul><li>velocity = wavelength * frequency </li></ul>The Wave Equation
  26. 26. Unit 1 - Waves <ul><li>velocity = wavelength * frequency </li></ul><ul><li>  </li></ul><ul><li>The above equation is known as the wave equation. It states the mathematical relationship between the speed (v) of a wave and its wavelength (  ) and frequency (f). Using the symbols v,  , and f, the equation can be rewritten as </li></ul><ul><li>v = f  </li></ul>The Wave Equation
  27. 27. Unit 1 - Waves <ul><li>Recall &quot;a wave is a disturbance moving through a medium.&quot; There are two distinct objects in this phrase - the &quot;wave&quot; and the &quot;medium.&quot; The medium could be water, air, or a slinky. These media are distinguished by their properties - the material they are made of and the physical properties of that material such as the density, the temperature, the elasticity, etc. Such physical properties describe the material itself, not the wave . </li></ul>What variables affect the speed at which a wave travels through a medium?
  28. 28. Unit 1 - Waves <ul><li>Waves are distinguished from each other by their properties - amplitude, wavelength, frequency, etc. These properties describe the wave, not the material through which the wave is moving. </li></ul><ul><li>Only an alteration in the properties of the medium will cause a change in the speed. </li></ul>What variables affect the speed at which a wave travels through a medium?
  29. 29. Unit 1 - Waves What variables affect the speed at which a wave travels through a medium?