The velocity of sound waves 'v' through a medium may be assumed to depend on :
(i) the density of the medium 'd' and (ii) the modulus of elasticity 'E' .
Deduce by the method of dimensions the formula for the velocity of sound . Take dimensional constant K=1.

The velocity (v) of sound through a medium may be assumed to depend on the density (rho) of the medium and modulus of elasticity (E). If the dimensions for elasticity (ratio of stress to strain) are [ML^(-1)T^(-2)] then deduce by the method of dimensions the formula for the velocity of sound is

The time period 'T' of a body executing SHM may be supposed to depend upon (i) the amplitude 'A' , (ii) the force constant 'k' and (iii) the mass 'm' . Deduce by the method of dimensions the formula for T.

The velocity upsilon of sound waves in a medium may depend upon modulus of elasticity (E ), density (d) and wavelength (lambda) of of the waves. Use method of dimensions to deerive the formula for upsilon.

The velocity of water wave v may depend on their wavelength lambda , the density of water rho and the acceleration due to gravity g . The method of dimensions gives the relation between these quantities as

Speed of sound wave in a fluid depends upon Directly on density of the medium Square of bulk modulus of the medium Inversely on the square root of density Directly on the square root of bulk modulus of the medium

The velocity of sound (upsilon) in a gas depends upon coefficint of volume elesticity E of the gas and density d of the gas. Use method of dimensions to derive the formula for upsilon.

The wavalenght (lambda) of matter waves may depends upon Planck's constant (h) mass (m) and velocity (upsilon) of the particle. Use the method of dimensions to derive the formula

Find relationship between speed of sound in a medium (v), the elastic constant (E) and the density of the medium (rho) .

Discuss the dependence of velocity of sound on temperature and density of a medium.