Question

Loudness of sound is directly proportional to the square of:
A) Amplitude of the wave
B) Distance from the source of sound
C) Frequency of the wave
D) Wavelength of the wave

Answer 1

Hint: When someone needs to tell you something personal the must come closer to your ear to whisper.
Sound waves need a medium to travel and we know that whenever something needs a medium to travel its energy deteriorates over the distance and eventually the wave loses all energy and dies. The energy of the wave depends on the source of the wave.

Complete solution:
The loudness of a sound wave is determined by its association with the amplitude, all types of waves have a certain amplitude.
The loudness of a sound depends on the amplitude of the sound wave. If the amplitude of the sound wave is large, then the sound is said to be loud.
It is expressed in decibel (dB).
Sounds above 80 dB become noise to human ears.
Refer to the following table.
Normal Breathing $\to$ 10 dB
Soft Whisper (at 5 m) $\to$ 30 dB
Normal Conversation $\to$ 60 dB
Busy Traffic $\to$ 70 dB
Average Factory $\to$ 80 dB
Here the height on the crust of height of the trough is called the amplitude of the wave and the amplitude of waves tells us the amount of energy the wave poses
Sound is a pressure wave caused when something vibrates, making particles hit into each other and then apart. The particles vibrate back and forth in the direction that the wave travels but do not get carried along with the wave. Loudness relates to the maximum pressure produced as particles are pressurized together as they are made to vibrate. This is also related to the maximum distance particles are moved from their normal position as they vibrate
The following relation is obeyed by a sound wave
$E \propto {A^2}$
Where,
$E$- Energy of the sound wave
$A$- Amplitude of the sound wave
If a wave has a greater amplitude it will have higher energy i.e., particles will be vibrating with higher energy and will impact our eardrums with greater force, so the wave will be loud
Similarly, on the other hand, if a wave is having lower amplitude its particle will be having lower energy, and the impact on our eardrums will be lesser hence loudness of the wave will be reduced.

The correct option is (A), The Loudness of sound is directly proportional to the square Amplitude of the wave.

Note: The spikes of amplitude will gradually decrease as the sound wave progresses, thus we see that the loudness of the sound decreases when we move away from the source.
The spikes on the upper and lower side of the reference line of a wave diagram show us the displacement of the atom of the object caused during its vibration about the mean position.
In a sound wave atom vibrates about their mean position they do not go along the wave they just pass on their energy to the neighboring atom and this cycle continues.
During this transfer of energy from one atom to another atom some part of the energy is used to free that atom from Vander wall`s force so we see some reduction in the amount of energy transferred and thus after some distance the all the energy is consumed to overcome Vander wall`s force and the particle has no energy to vibrate this wave dies and no sound is not propagated.