Sound Wave-
Before you go through this article, make sure that you have gone through the previous article on Sound Waves.
We have learnt that-
- Sound is a mechanical three dimensional and longitudinal wave.
- It is described in two ways-
- Displacement wave form
- Pressure wave form
In this article, we will learn about speed of sound wave in fluids.
Speed of Sound Wave In A Fluid (Liquid or Gas)-
The speed of sound wave (longitudinal wave) through a fluid is determined by the following two factors-
1. Volume elasticity or Bulk modulus (K) of the fluid-
- It determines the fractional change in volume (ΔV/V) when pressure is changed by ΔP.
2. Density of the fluid
- It determines its inertia.
Deriving Expression For Speed of Sound Wave-
We can use method of dimensions to derive an expression for the speed (v) of the longitudinal waves.
(Equation-01)
By the principle of homogeneity, we must have-
On comparing the dimensions of each term on LHS and RHS, we have-
Using in Equation-01, we get-
This is the expression for speed of a longitudinal wave in a fluid.
It is important to note that-
- A given solid or a liquid has a fixed value of bulk modulus but so is not the case for gases.
- The value of bulk modulus of a gas depends on the process.
To express the above formula in terms of commonly used parameters like pressure (P) and temperature (T), we need to know what kind of process an element of gas undergoes when a sound wave travels through it.
Test Your Concepts-
Speed of Sound Wave in A Fluid
Next Article-
Newton’s Formula For Speed of Sound in Gas
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