Question

The amplitude of a sound wave is increased from $1mm$ to $2mm$. The loudness of the sound will:

• A. increase two times
• B. increase four times
• C. same
• D. decrease

Answer 1

The correct option is B

increase four times

Explanation for the correct options:

B) increase four times

• The loudness of a sound is directly proportional to the square of the amplitude.
• That is, $Loudness\propto {\left(Amplitude\right)}^2$
• So, if the amplitude is doubled then loudness will be$4$times.

Explanation for the incorrect option:

A) increase two times

• The loudness of a sound is directly proportional to the square of the amplitude.
• That is, $Loudness\propto {\left(Amplitude\right)}^2$
• So, if the amplitude is same then loudness will become same.

C) Same

• The loudness of a sound is directly proportional to the square of the amplitude.
• That is, $Loudness\propto {\left(Amplitude\right)}^2$
• So, if the amplitude is the same as the loudness will become the same.

D) Decrease

• The loudness of a sound is directly proportional to the square of the amplitude.
• That is, $Loudness\propto {\left(Amplitude\right)}^2$
• So, if the amplitude is decreased then loudness will become decrease.
  

Therefore, the amplitude of a sound wave is increased from $1mm$to $2mm.$ The loudness of the sound will increase four times (Option B).