Question

For hearing the loudest ticking sound heard by the ear, find the angle x in the given figure.

$\text{A}\text{. }{{30}^{\circ }}$
$\text{B}\text{. 4}{{0}^{\circ }}$
$\text{C}\text{. 5}{{0}^{\circ }}$
$\text{D}\text{. 6}{{0}^{\circ }}$

Answer 1

Hint: Sound is a wave produced due to vibrations of the air molecules. Since sound is wave it reflects when it hits a surface. Here, the sound waves are sent through a tube. The loudest sound will be heard when the angle x is equal to the angle of incidence.

Complete step-by-step answer:
Let us first understand what sound is and what its properties are.
Sound is a wave produced due to the vibrations of the air molecules. The vibrations of the air molecules are produced by a vibrating sound. When an object vibrates, it also vibrates the air molecules that travel in the form of a wave. The wave reaches our ear and vibrates our eardrum, which causes a sensation. Hence, we say that we hear a sound from the source.
Since sound is wave like light, it also reflects when it hits an obstacle or when there is a change in the surrounding medium. Therefore, sound also obeys the laws of reflection. We sound that for light the angle of incidence and angle of refraction to the normal drawn to the surface of reflection.
In this case, the sound is made to travel through tubes. That means we can consider the sound as a ray. Therefore, for the loudest sound, the second tube must be held in such a way that the reflected sound passes through it. That means that the angle x must be equal to the angle of reflection. Therefore, x must be equal to the angle of incidence.
As we can see in the figure, the ray is making an angle of incidence i. And $i=90-50={{40}^{\circ }}$.
This means that x = ${{40}^{\circ }}$

So, the correct answer is “Option B”.

Note: Note that sound is not a ray. Meaning, sound does not travel in a straight line. Since sound is wave, it spreads in all the directions when the source emits the sound.
The loudness of the sound decreases as the distance of the listener from the source increases.