Answer:
Amplitude is decreased by a factor of [tex]\sqrt3[/tex] if intensity is decreased by a factor of 3.
Explanation:
Intensity of a sound wave is directly proportional to the square of its amplitude.
Therefore, if intensity is [tex]I[/tex] and amplitude is [tex]A[/tex], then
[tex]I=kA^2[/tex], where, [tex]k[/tex] is constant of proportionality.
Now, if intensity of sound wave is decreased by a factor of 3. So,
New intensity is, [tex]I_{new}=\frac{I}{3}[/tex]
[tex]I_{new}=kA_{new}^2\\\frac{I}{3}=kA_{new}^2[/tex]
Plug in [tex]kA^2[/tex] for [tex]I[/tex]. This gives,
[tex]\frac{kA^2}{3}=kA_{new}^2\\A_{new}^2=\frac{A^2}{3}\\A_{new}=\sqrt{\frac{A^2}{3}}=\frac{A}{\sqrt{3}}[/tex]
Therefore, amplitude is decreased by a factor of [tex]\sqrt3[/tex].
