What is the relationship between velocity, frequency and wavelength?

  1. What is the relationship between velocity, frequency and wavelength?
    • Calculate the wavelength of sound for frequencies upto 130 kHz at which a bat can hear it. [Take, speed of sound = 344 ms–1]
    • Express the audible range of frequencies in terms of time-period, if the velocity of sound in air is 330 ms–1.
  1. Relationship between velocity, frequency and wavelength are as follows:
    image
    image …(1)
    and
    image
    ⇒ Put the value of f in Eq. (1), we get
    Then, ν = λf
    velocity = Frequency x Wavelenght
    • We know that,
      ∵ Frequency, f = image
      Given, velocity of sound in air, v = 344ms–1
      Frequency, f = 130 kHz = 130000 Hz
      Wavelength, λ = image [from Eq.(2)]
      image
    • Audible range of frequencies are, v1 = 20 Hz, v2 = 20000 Hz and
      velocity of sound in air, v = 330 ms–1
      Time period, (T1) = image
      T2 = image
      Thus, audible range lies between 5 x 10–2s to 5 x 10–5sin terms of time-period.