Question

The air pressure at sea level is $101325 \,Pa$ . At the centre of a rarefaction of a sound wave in air, the pressure is $91000 \,Pa$ . Which is the most likely pressure at the centres of a compression of the same wave?

• A. $91000\, Pa$
• B. $101000\, Pa$
• C. $111650\, Pa$
• D. $121000\, Pa$

Answer 1

Answer: (C)

$111650\, Pa$

Answer 2

Given, air pressure, $p_{o}=10135\,p_{a}$ and pressure at the centre of rarefaction, $p_{1}=91000\,pa$
As we know that, during the propagation of sound wave in air pressure varies as

Thus, we have
$p_{1}=p_{0}-dp$
$91000=101325-dp$ (putting values)
$\therefore dp=101325-91000$
$=10325\,pa$
Thus, the pressure at the centre of compression
$p_{1}=p_{0}+dp$
$=101325+10325$
$=111650\,Pa$
Therefore, the most appropriate option is (c)