Mechanical waves

Question 1

Laplace and Newtons formula

Answer 1

Newton said that the velocity of shoud follows isothermal process whereas the laplace said it follows adiabatic process.

Question 2

Laplace and Newtons formula Prove

Answer 2

In laplace gama is used where as in newtons only PV=0 is used.
For newton
PdV+VdP=o
V=volumetric stress/volumetric strain
v=√B/ρ so over all velocity of sound is 280m/s
For Laplace
γPV^ γ-1.dV+V^ γ dP =0
γP=-Badi
v=√Badi/ρ=√γP/ρ so overall velocity of sound is 331.2m/s.

Question 3

Relation of velocity with density mass and temperature.

Answer 3

FOR temp and mass
PV=RT
V=M/ρ
PM/ρ=RT
P/ρ=RT/M
v=√γP/ρ =√γRT/M so it proves that velocity of sound is inversely propotional to mass whereas directly propotional to the temp.
For density
v=√γP/ρ so this proves that velocity of sound is inversely propotional to density.

Question 4

Why velocity of sound is more in solid than that of liquid or gas?

Answer 4

Because the velocity of the sound depends upon the bulk modulus/ elasticity and density i.e v=√B/ρ since √B/ρ of solid is greater than that of liquid or gas the velocity is greater in short vsolid>vliquid>vgas.

Question 5

Why does the sound travel faster in night time?

Answer 5

Because the density of air in night time is less compared to day time.

Question 6

Formula for numerical

Answer 6

v1/v2=T1/T2