Question

State two factors on which the speed of wave travelling in a medium depends.

Answer 1

Hint: To solve this question, we have to remember some basic points of the speed of waves. The speed of a sound travelling in a medium increases when the stiffness (the resistance of an elastic body to deformation by an applied force) of the material decreases if the density increases.

Complete step-by-step answer:
As we know that, the speed of a wave travelling through a medium is defined as the distance travelled per unit time by that wave as it propagates through the medium. It depends strongly on the temperature as well as the medium through which the wave is propagating.
The speed of a sound wave can be represented by c in mathematical notations.
The speed of wave can be given by the Newton-Laplace equation as:
$ \Rightarrow c = \sqrt {\dfrac{{{K_S}}}{\rho }} $,
Where c = speed of wave,
             ${K_S}$ = coefficient of stiffness.
             $\rho $ = density of the medium.
Thus, we can say that the speed of wave travelling in medium depends on the stiffness and density of the medium.
As we know that, stiffness is the resistance of an elastic body to deformation by an applied force.
And, we also know that the resistance of a material increases when the temperature increases.
So, the speed of the wave increases with increase in temperature and decreases with increase in density.
Hence, finally we can say that the speed of wave travelling in a medium depends on the temperature and the density of that medium.

Note: Whenever we ask such questions, we have to remember the basic formula and representation of the speed of the wave. The speed of a sound wave in an ideal gas depends only on the temperature and composition of the medium. The speed of waves has a weak dependence on the frequency and pressure. Wave travels most slowly in gases, faster in liquids and still faster in solids.