How are the wavelength and frequency of a sound wave related to its speed ?

Explanation

From the definition, No of waves produced in Ts=1
Then, No of waves produced in 1s `= (1)/(T)`
Therefore, frequency `(v)= (1)/(T) s^(-1)`
We also know, that Distance travelled by one complete wave `=lamda`
Time taken to complete one wave =Ts
So, Distance travelled in `1s = (lamda)/(T)`
But, distance travelled in 1s is speed (v). `v=(lamda)/(T)= lamda v (because (1)/(T)=v)`
`v= lamda v`
So, wave speed= Wavelength `xx` Frequency. The equation `v= lamda v`, is called as the wave equation. The speed of sound remains same for all frequences a given medium under the same physical conditions.