establish the relationship between speed of sound, its wavelength and frequency?
Let the speed of sound be V. Its wavelength be λ and the frequency be ν.
The time period of the wave is given by, T = 1/ν
In time T the wave covers a distance of one wavelength λ.
Therefore, speed of sound, V = λ/T = νλ
Thus we have, V = νλ
Or, Speed = Frequency × Wavelength
let the time period be T seconds.
IN T sec. , the no. of waves generated = 1. so , in 1 sec. no. of waves generated = 1 / T
no. of waves generated in 1 sec. is frequency.
therefore, frequency = 1 / T
now, velocity = distance travelled / time taken
= v = wavelength / T
= v = frequency x wavelength