Question

The energy per unit area associated with a progresive sound wave will be doubled if:

• A. The amplitude of the wave is doubled
• B. The amplitude of the wave is increased by 50%
• C. The amplitude of the wave is increased by 41%
• D. The frequency of the wave is increased by 41%

Answer 1

Answer: (C), (D)

The correct options are
C The amplitude of the wave is increased by 41%
D The frequency of the wave is increased by 41%

The energy of a progressive wave is given by

$E=2\rho A^2{\pi }^2{f}^2$. . . . . . .(1)

where $f=$ frequency of the wave

$A=$ amplitude of the wave

$\rho =$ density

from equation (1),

$E\propto \rho$

$E\propto A^2$

$E\propto f^2$

Given,

$\frac{E_1}{E_2}=\frac{A_1^2}{A_2^2}=\frac{1}{2}$

$\frac{A_1}{A_2}=\frac{1}{\sqrt{2}}$

$A_2=\sqrt{2}{A}_1$
$A_2=(1+0.40)A_1=1.41A_1$

Similarly, when frequency $f_2=\sqrt{2}{f}_1=(1+0.40)f_1=1.41f_1$, we get the same relation.
The energy per unit area associated with a progressive sound wave will be double, if the amplitude and the frequency of the wave are increased by 41%.