Question

A source of sound is in the shape of a long narrow cylinder radiating sound waves normal to the axis of the cylinder. Two points $P$ and $Q$ are at perpendicular distances of $9 \mathrm{m}$ and $25 \mathrm{m}$ from the axis. The ratio of the amplitudes of the waves at $P$ and $Q$ is
(a) 5: 3
(b) $\sqrt{5}: \sqrt{3}$
(c) 3: 5
(d) 25: 9

Answer 1

Hint: We know that sound waves are longitudinal waves that travel through a medium like air or water. When we think about sound, we often think about how loud it is (amplitude, or intensity) and its pitch (frequency). Sound is a mechanical wave that results from the back and forth vibration of the particles of the medium through which the sound wave is moving. The motion of the particles is parallel (and anti-parallel) to the direction of the energy transport. This is what characterizes sound waves in air as longitudinal waves.

Complete step by step answer
We can say that sound waves are travelling vibrations of particles in media such as air, water or metal. So, it stands to reason that they cannot travel through empty space, where there are no atoms or molecules to vibrate. Sound waves do not live forever. As the energy of the sound is transferred to more and more molecules of air, they vibrate less and less until the effect is lost in the constant random jostle of air molecules.
In general, soft, pliable, or porous materials (like cloths) serve as good acoustic insulators - absorbing most sound, whereas dense, hard, impenetrable materials (such as metals) reflect most. How well a room absorbs sound is quantified by the effective absorption area of the walls, also named total absorption area.
$I \propto A^{2}$ and $I \propto \dfrac{1}{2} \pi R L$
$\dfrac{I_{1}}{I_{2}}=\dfrac{R_{2}}{R_{1}}=\dfrac{A_{1}^{2}}{A_{2}^{2}} \Rightarrow \dfrac{A_{1}}{A_{2}}=\sqrt{\dfrac{R_{2}}{R_{1}}}=\sqrt{\dfrac{25}{9}}=5: 3$

So, the correct option is Option A.

Note: We know that Sound waves in air (and any fluid medium) are longitudinal waves because particles of the medium through which the sound is transported vibrate parallel to the direction that the sound wave moves. Sound has two basic forms: acoustic energy and mechanical energy. Each type of sound has to be tackled in their own way. Acoustic energy or sound is what we experience every day. It is in fact vibration of air (sound waves) which is transformed by the tympanic membrane in the ear of humans to audible sounds.