Edexcel IGCSE Physics: Double Science 复习笔记： 3.1.3 The Wave Equation

• All waves obey the wave equation, which is used to calculate the wave speed:

• Where:
  • v = wave speed in metres per second (m/s)
  • f = frequency in Hertz (Hz)
  • λ = wavelength in metres (m)

   

• The wave speed equation may need to be rearranged, which can be done using this formula triangle:

• The equation which relates the frequency of a wave to its time period is:

• Where:
  • T = time period, measured in seconds (s)
  • f = frequency, measured in Hertz (Hz)

   

Step 1: List the known values

• • Frequency, f = 6 × 10¹⁴ Hz

   

Step 2: State the relationship between frequency and time period 

• • This question involves quantities of time and frequency, so the equation which relates time period and frequency of a wave is:

   

Step 3: Substitute the known values in to the equation and calculate the time period 

T = 1 ÷ (6 × 10¹⁴) = 1.67 × 10^-15 s

• • Therefore, it takes 1.67 × 10^-15 s (to 2 decimal places) for one wave of visible light to pass our eyes

   

• The wave equation can be applied and rearranged to calculate properties of waves, such as:
  • wave speed
  • frequency
  • time period

   

• The wave equation applies to all types of wave, including sound waves and electromagnetic waves

Part (a)

Step 1: List the known quantities

• • Time period, T = 0.0001 s

   

Step 2: Write out the equation relating time period and frequency

Step 3: Rearrange for frequency, f, and calculate the answer

f = 1 ÷ T = 1 ÷ 0.0001

Frequency, f = 10 000 Hz = 1 × 10⁴ Hz

Part (b)

Step 1: List the known quantities

• • Wave speed, v = 330 m/s
  • Frequency, f = 1 × 10⁴ Hz

   

Step 2: Write out the wave speed equation

v = f × λ

Step 3: Rearrange the equation to calculate the wavelength

λ = v ÷ f

Step 4: Use the frequency you calculated in part (a) and put the values into the equation

λ = 330 ÷ 1 × 10⁴

Wavelength, λ = 0.033 m

Step 1: List the known quantities

• • Frequency, f = 200 kHz = 200 000 Hz
  • Wavelength, λ = 1500 m

   

Step 2: Write out the wave speed equation

• • This question requires wave speed, so state the equation linking wave speed, wavelength and frequency:

   

v = f × λ

Step 3: Substitute the known values to calculate the wave speed 

v = 200 000 × 1500 = 300 000 000 = 3 × 10⁸

Step 4: State the unit with the answer

• • The units for speed are m/s
  • Therefore, the speed of these radio waves is 3 × 10⁸ m/s