IB DP Physics: SL复习笔记4.2.1 Properties of Waves

Properties of Waves

  • Travelling waves are defined as follows:

Oscillations that transfer energy from one place to another without transferring matter

  • Energy is transferred by the waves, but matter is not
  • The direction of the motion of the wave is the direction of the energy transfer
  • Travelling waves can be of two types:
    • Mechanical Waves, which propagate through a medium and cannot take place in a vacuum
    • Electromagnetic Waves, which can travel through a vacuum
  • Waves are generated by oscillating sources
    • These oscillations travel away from the source
  • Oscillations can propagate through a medium (e.g. air, water) or in vacuum (i.e. no particles), depending on the type of wave
  • The key properties of travelling waves are as follows:
  • 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
    • Measured in metres (m)
  • Wavelength (λ) is the length of one complete oscillation measured from same point on two consecutive waves
    • For example, two crests, or two troughs
    • Measured in metres (m)
  • Amplitude (x0) is the maximum displacement of an oscillating wave from its equilibrium position (x = 0)
    • Amplitude can be positive or negative depending on the direction of the displacement
    • Measured in metres (m)
  • Period (T) is the time taken for a fixed point on the wave to undergo one complete oscillation
    • Measured in seconds (s)
  • Frequency (f) is the number of full oscillations per second
    • Measured in Hertz (Hz)
  • Wave speed (c) is the distance travelled by the wave per unit time
    • Measured in metres per second (m s-1)

7.1.1.2-Amplitude-and-wavelength

Diagram showing the amplitude and wavelength of a wave

  • The frequency, f, and the period, T, of a travelling wave are related to each other by the equation:

2.1.1.3-Frequency-period-equation

4-2-1-period-and-frequency_sl-physics-rn

Period T and frequency f of a travelling wave

Worked Example

The graph below shows a travelling wave.

4-2-1-we-properties-of-wave-question-graph

Determine:

(i) The amplitude A of the wave in metres (m)

(ii) The frequency f of the wave in hertz (Hz)

(i) Identify the amplitude A of the wave on the graph

    • The amplitude is defined as the maximum displacement from the equilibrium position (x = 0)
4-2-1-we-properties-of-wave-step-1

    • The amplitude must be converted from centimetres (cm) into metres (m)
A = 0.1 m

(ii) Calculate the frequency of the wave

Step 1: Identify the period T of the wave on the graph

    • The period is defined as the time taken for one complete oscillation to occur

4-2-1-we-properties-of-wave-step-2

    • The period must be converted from milliseconds (ms) into seconds (s)

T = 1 × 10–3 s

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

Frequency-and-Period-Relationship

Step 3: Substitute the value of the period determined in Step 1

Properties-of-Waves-Worked-Example-Frequency-Calculation

f = 1000 Hz

The Wave Equation

  • The wave equation describes the relationship between the wave speed, the wavelength and the frequency of the wave

c = fλ

  • Where
    • c = wave speed in metres per second (m s−1)
    • f = frequency in hertz (Hz)
    • λ = wavelength in metres (m)

Deriving the Wave Equation

  • The wave equation can be derived using the equation for speed
  • Where
    • v = velocity or speed in metres per second (m s−1)
    • d = distance travelled in metres (m)
    • t = time taken in seconds (s)
  • When the source of a wave undergoes one complete oscillation, the travelling wave propagates forward by a distance equal to one wavelength λ
  • The travelling wave covers this distance in the time it takes the source to complete one oscillation, the time period T
  • Therefore, combining these equations gives the wave equation

c = fλ

Worked Example

A travelling wave has a period of 1.0 μs and travels at a velocity of 100 cm s–1. Calculate the wavelength of the wave. Give your answer in metres (m).

Step 1: Write down the known quantities

    • Period, T = 1.0 μs = 1.0 × 10–6 s
    • Velocity, c = 100 cm s–1 = 1.0 m s–1

Note the conversions:

    • The period must be converted from microseconds (μs) into seconds (s)
    • The velocity must be converted from cm s–1 into m s–1

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

Frequency-and-Period-Relationship

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

The-Wave-Equation-Worked-Example-Frequency-Calculation

f = 1.0 × 106 Hz

Step 4: Write down the wave equation

c = fλ

Step 5: Rearrange the wave equation to calculate the wavelength λ

Wave-Equation-for-the-Wavelength

Step 6: Substitute the numbers into the above equation

The-Wave-Equation-Worked-Example-Wavelength-Calculation

λ = 1 × 10–6 m

 

 

 

 

转载自savemyexams

更多IB课程
翰林国际教育资讯二维码