Question

If the amplitude of sound is doubled and the frequency reduced to one-fourth, the intensity of sound at the same point will be

• A. Increased by a factor of 2
• B. Decreased by a factor of 2
• C. Decreased by a factor of 4
• D. Unchanged

Answer 1

Answer: (C)

Decreased by a factor of 4

Answer 2

$I = 2\pi^{2}a^{2}n^{2}v\rho$ ⇒ $I \propto a^{2}n^{2}$ ⇒ $\frac{I_{1}}{I_{2}} = \left( \frac{a_{1}}{a_{2}} \right)^{2} \times \left( \frac{n_{1}}{n_{2}} \right)^{2}$

$= \left( \frac{1}{2} \right)^{2} \times \left( \frac{1}{1/4} \right)^{2} \Rightarrow I_{2} = \frac{I_{1}}{4}$

($I = 2\pi^{2}a^{2}n^{2}v\rho$ ⇒ $I \propto a^{2}n^{2}$ ⇒ $\frac{I_{1}}{I_{2}} = \left( \frac{a_{1}}{a_{2}} \right)^{2} \times \left( \frac{n_{1}}{n_{2}} \right)^{2}$

$= \left( \frac{1}{2} \right)^{2} \times \left( \frac{1}{1/4} \right)^{2} \Rightarrow I_{2} = \frac{I_{1}}{4}$)