6.1.3 The Wave Equation

• What is the wave equation?

  The wave equation is expressed as $v =$$f \times \lambda$
• What does $v$ represent in the wave equation?


  $v$ is the wave speed, measured in meters per second (m/s).
• What does $f$ represent in the wave equation?


  $f$ is the frequency of the wave, measured in Hertz (Hz).
• What does $\lambda$ represent in the wave equation?


  $\lambda$ (lambda) is the wavelength, measured in meters (m).
• How does the speed of a wave vary with the medium?

  Different types of waves travel at different speeds depending on the medium.
• What happens to wavelength when frequency increases while wave speed remains constant?

  Increasing frequency while keeping speed constant will decrease wavelength.
• What are the definitions of wave speed, frequency, and wavelength?

  • Wave Speed (v): The speed at which the wave travels through a medium.
  • Frequency (f): The number of complete waves (cycles) that pass a point in one second.
  • Wavelength (λ): The distance between two consecutive points that are in phase on the wave.
• What are the steps to use the wave equation effectively?

  1. Identify the Known Values: Determine given quantities (wave speed, frequency, wavelength).

  2. Rearrange the Equation if Necessary: Solve for a specific variable.

  3. Substitute the Known Values: Plug values into the equation.

  4. Solve for the Unknown: Calculate the missing value.
• How do you rearrange the wave equation to find frequency?

  To find frequency, rearrange it to $f =$$\frac{v}{\lambda}$.
• How do you rearrange the wave equation to find wavelength?

  To find wavelength, rearrange it to $\lambda =$$\frac{v}{f}$.
• What is the wave speed of a wave with a frequency of 50 Hz and a wavelength of 0.2 meters?

  The wave speed is $10 \, \text{m/s}$.
• What is the wavelength of a sound wave traveling at 340 m/s with a frequency of 1700 Hz?

  The wavelength is $0.2 \, \text{m}$.
• What is the frequency of a water wave traveling at 2 m/s with a wavelength of 0.5 meters?

  The frequency is $4 \, \text{Hz}$.
• What are common pitfalls when using the wave equation?

  • Unit Mismatch: Ensure all quantities are in correct units.
  • Incorrect Rearrangement: Be careful when rearranging the equation.
  • Understanding the Physical Meaning: Recognize the impact of changing variables.
• What are some applications of the wave equation?

  • Sound Waves: Calculate how different frequencies travel in various media.
  • Light Waves: Determine the wavelength of light waves.
  • Water Waves: Analyze wave patterns and speeds in oceans or lakes.
• What is the wave speed of a radio wave traveling at $3 \times 10^8 \, \text{m/s}$ with a frequency of 100 MHz?


  To find the wavelength, use the wave equation.
• What is the frequency of a light wave with a wavelength of 600 nm and a speed of $3 \times 10^8 \, \text{m/s}$?


  To find the frequency, use the wave equation.
• What is the frequency of a seismic wave traveling at 5000 m/s with a wavelength of 200 meters?

  To find the frequency, use the wave equation.
• What is the summary of the wave equation?

  • The wave equation $v =$$f \times \lambda$ relates wave speed, frequency, and wavelength.
  • Mastering this equation helps solve various wave motion problems.
  • Regular practice reinforces understanding for exams.