Question

Derive the expression of 1 effect of pressure on velocity of sound 2. Effect of temperature on speed of sound 3 effect of humidity on speed of sound​

Answer 1

Explanation:

1. pressure dosent affect speed of sound.

2. V is directly proportional to root T

3. as humidity increases speed also increases.

Answer 2

Answer:

With the increase in pressure velocity of sound increases, with the increase in temperature the velocity of sound increases, and the velocity of sound decreases with the increase of humidity of the air or vice-versa.

Explanation:

Let's derive the expressions one by one.

(i) Effect of pressure on the speed of sound

The velocity of sound(V) is given as;

V=$($γB$/$ρ$)^{1/2}$       (1)

Where,

γ=adiabatic constant of the medium

B=bulk modulus of the medium

ρ=density of the medium

B=-ΔPV$/$ΔV=P    (2)

P=pressure

-ΔV$/$V= volumetric strain

By putting equation (2) in equation (1) we get;

V=$($γP$/$ρ$)^{1/2}$  (3)

V∝$($P$)^{1/2}$       (4)

(ii) Effect of temperature on the speed of sound

V=$($γP$/$ρ$)^{1/2}$          

Ideal gas equation,

PV=RT     (5)

P=pressure

V=volume

R= universal gas constant

T=temperature

V=M$/$ρ    (6)

By putting equation (6) in equation (5) we get;

P×M$/$ρ =RT

P$/$ρ=RT/M    (7)

Putting equation (7) in equation (3) we get;

V=$($γRT$/$M$)^{1/2}$  (8)

V∝$($T$)^{1/2}$        (9)

(iii)Effect of humidity on the speed of sound

From equation (3) we have;

V=$($γP$/$ρ$)^{1/2}$

where,

γP=constant

Then the equation becomes,

V∝$($1$/$ρ$)^{1/2}$  (10)

We know that more humid air has more density. So, from equation (10) we conclude that the velocity of sound decreases with the increase of humidity of the air or vice-versa.

Hence by the above equations, we conclude that with the increase in pressure velocity of sound increases, with the increase in temperature the velocity of sound increases, and the velocity of sound decreases with the increase of humidity of the air or vice-versa.