IB DP Physics: SL复习笔记4.1.1 Properties of Oscillations

Describing Oscillations

  • An oscillation is defined as follows:

The repetitive variation with time t of the displacement x of an object about the equilibrium position (x = 0)

4-1-1-graphing-oscillations_sl-physics-rn

A pendulum oscillates between A and B. On a displacement-time graph, the oscillating motion of the pendulum is represented by a wave, with an amplitude equal to x0

  • Displacement (x) of a wave is the distance of a point on the wave from its equilibrium position
    • It is a vector quantity; it can be positive or negative and it is measured in metres (m)
  • Period (T) or time period, is the time interval for one complete repetition and it is measured in seconds (s)
    • If the oscillations have a constant period, they are said to be isochronous

7.1.1.2-Displacement-time-wave

Diagram showing the time period of a wave

  • Amplitude (x0) is the maximum value of the displacement on either side of the equilibrium position is known as the amplitude of the oscillation
    • Amplitude is measured in metres (m)
  • Wavelength (λ) is the length of one complete oscillation measured from the same point on two consecutive waves
    • Wavelength is measured in metres (m)

7.1.1.2-Amplitude-and-wavelength

  • Frequency (f) is the number of oscillations per second and it is measured in hertz (Hz)
    • Hz have the SI units of per second s−1
  • The frequency and the period of the oscillations are related by the following equation:

2.1.1.3-Frequency-period-equation

Phase & Phase Difference

  • Phase is a useful way to think about waves
  • The phase of a wave can be considered in terms of:
    • Wavelength
    • Degrees
    • Radians
  • One complete oscillation is:
    • 1 wavelength
    • 360°
    • 2π radians

4-2-1-wavelength-and-amplitude_sl-physics-rn

Wavelength λ and amplitude A of a travelling wave

  • The phase difference between two waves is a measure of how much a point or a wave is in front or behind another
  • This can be found from the relative position of the crests or troughs of two different waves of the same frequency
    • When the crests of each wave, or the troughs of each wave are aligned, the waves are in phase
    • When the crest of one wave aligns with the trough of another, they are in antiphase
  • The diagram below shows the green wave leads the purple wave by ¼ λ

7.1.1.2.5-Phase-difference

Two waves ¼ λ out of phase

  • In contrast, the purple wave is said to lag behind the green wave by ¼ λ
  • Phase difference is measured in fractions of a wavelength, degrees or radians
  • The phase difference can be calculated from two different points on the same wave or the same point on two different waves
  • The phase difference between two points can be described as:
    • In phase is 360o or 2π radians
    • In anti-phase is 180o or π radians

Worked Example

A child on a swing performs 0.2 oscillations per second.Calculate the period of the child's oscillations.

Step 1: Write down the frequency of the child's oscillations

f = 0.2 Hz

Step 2: Write down the relationship between the period T and the frequency f

Period-and-Frequency-Relationship

Step 3: Substitute the value of the frequency into the above equation and calculate the period

T = 5 s

Worked Example

Plane waves on the surface of water at a particular instant are represented by the diagram below.WE-Wave-properties-question-image

The waves have a frequency of 2.5 Hz.Determine:

a) The amplitude

b) The wavelength

c) The phase difference between points A and B

7.1.1.2-Worked-example-wave-properties-2_2

Exam Tip

When labelling the wavelength and time period on a diagram:

  • Make sure that your arrows go from the very top of a wave to the very top of the next one
  • If your arrow is too short, you will lose marks
  • The same goes for labelling amplitude, don’t draw an arrow from the bottom to the top of the wave, this will lose you marks too.

 

 

 

 

 

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