What is the relationship between velocity, frequency and wavelength?

[LokeshCBSE]

1. What is the relationship between velocity, frequency and wavelength?
2. • 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.

[LokeshCBSE]

1. Relationship between velocity, frequency and wavelength are as follows:
   
   ∴ …(1)
   and
   
   ⇒ Put the value of f in Eq. (1), we get
   Then, ν = λf
   velocity = Frequency x Wavelenght
2. • We know that,
     ∵ Frequency, f =
     Given, velocity of sound in air, v = 344ms^–1
     Frequency, f = 130 kHz = 130000 Hz
     Wavelength, λ = [from Eq.(2)]
     
   • Audible range of frequencies are, v1 = 20 Hz, v2 = 20000 Hz and
     velocity of sound in air, v = 330 ms^–1
     Time period, (T₁) =
     T₂ =
     Thus, audible range lies between 5 x 10^–2s to 5 x 10^–5sin terms of time-period.