If the amplitude of sound is doubled and the | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The intensity of a sound wave is given by the formula $I = 2{\pi ^2}{a^2}{n^2}\rho v$,where $a$ is the amplitude and $n$ is the frequency.From thi

Vedclass · Accepted Answer

Decreased by a factor of $4$

Vedclass · Answer

(C) The intensity of a sound wave is given by the formula $I = 2{\pi ^2}{a^2}{n^2}ho v$,where $a$ is the amplitude and $n$ is the frequency.From this,we see that $I \propto {a^2}{n^2}$.Let the initial amplitude be $a_1$ and frequency be $n_1$. Let the final amplitude be $a_2 = 2a_1$ and frequency be $n_2 = n_1/4$.The ratio of intensities is $\frac{I_2}{I_1} = \left( \frac{a_2}{a_1} ight)^2 	imes \left( \frac{n_2}{n_1} ight)^2$.Substituting the values: $\frac{I_2}{I_1} = (2)^2 	imes (1/4)^2 = 4 	imes (1/16) = 1/4$.Therefore,$I_2 = I_1/4$,which means the intensity is decreased by a factor of $4$.

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

Similar Questions

$A$ point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9 \ m$ and $25 \ m$ respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

$A$ sound source emits sound waves in a uniform medium. If energy density is $E$ and maximum speed of the particles of the medium is ${v_{\max }}$,the plot between $E$ and ${v_{\max }}$ is best represented by

Which of the following statements is correct?

Two waves represented by the following equations are travelling in the same medium: $y_1 = 5\sin 2\pi (75t - 0.25x)$ and $y_2 = 10\sin 2\pi (150t - 0.50x)$. The intensity ratio $I_1/I_2$ of the two waves is:

If the separation between the screen and the source is increased by $2\%$,what would be the effect on the intensity?

Vedclass Test Series

Exam Paper Generator

Online Exam Module