Physics, asked by thinkarduinoyt, 10 months ago

Q: How does the speed of sound in air changes with

a) rise in temperature of air, and
b) decrease in humidity in air?

(Students have to write weather the given factor will increase, decrease or will bring no change in speed of sound in air).

Answers

Answered by Anonymous

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ANSWER

speed of sound waves in air increases with increases in humidity because air density decreases with increase in humidity and The speed of sound in a medium is inversely proportional to the square root of its density.

Answered by sbtgta125

Answer:

a) Increase

b) Decrease

Explanation:

The speed of sound in air is given by the Laplace correction in Newton's formula, as

$v=\sqrt{\gamma\times P\over \rho}\\\\where,\\~~~~~~~~~~~\gamma=ratio~of~C_P~and~C_V~(constant~for~a~gas)\\~~~~~~~~~~~P=Pressure~of~gas\\~~~~~~~~~~~\rho=density~of~gas$

Since,

$PV=nRT\\\\and,~P={nRT\over V}$

This formula can also be written as

$v=\sqrt{\gamma\times P\over \rho}\\\\v=\sqrt{\gamma\times {nRT\over V}\over\rho}\\\\v=\sqrt{\gamma\times nRT\over \rho \times V}\\\\v=\sqrt{\gamma\times nRT\over M}~~~~~~~~(\rho\times V=M)$

Hence, on rising temperature, speed of sound in air increases as

$v$ ∝ $\sqrt T$

Now, average mass of air is about 29 g/mole.

And, that of humidity (H₂O) is 18 g/mole i.e., lower than that of air.

So, if humidity decreases in air, the average mass ( $M$ in the formula) of air increases, because humidity (having low mass) decreases the average mass of air when present in air.

Hence, on decreasing humidity, $M$ increases.

In the formula,

$v$ ∝ $1\over\sqrt M$

So, the velocity decreases.

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Q: How does the speed of sound in air changes with a) rise in temperature of air, and b) decrease in humidity in air? (Students have to write weather the given factor will increase, decrease or will bring no change in speed of sound in air).

Answers

ANSWER

Q: How does the speed of sound in air changes with

a) rise in temperature of air, and
b) decrease in humidity in air?

(Students have to write weather the given factor will increase, decrease or will bring no change in speed of sound in air).