(D) For a spherical wave emitted by a point source,the intensity $I$ at a distance $r$ is given by $I = \frac{P}{4 \pi r^2}$,where $P$ is the power of

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(D) For a spherical wave emitted by a point source,the intensity $I$ at a distance $r$ is given by $I = \frac{P}{4 \pi r^2}$,where $P$ is the power of the source.Since $I \propto A^2$,where $A$ is the amplitude,we have $A^2 \propto \frac{1}{r^2}$,which implies $A \propto \frac{1}{r}$.Let $A_P$ and $A_Q$ be the amplitudes at distances $r_P = 4 \ m$ and $r_Q = 9 \ m$ respectively.Then,the ratio of amplitudes is $\frac{A_P}{A_Q} = \frac{r_Q}{r_P}$.Substituting the given values,$\frac{A_P}{A_Q} = \frac{9}{4}$.

Class 11 Physics Waves and Sound Energy and Intensity of Waves

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$A$ stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $4 \ m$ and $9 \ m$ respectively from the source. The ratio of amplitudes of the waves at $P$ and $Q$ is

KCET 2009 All KCET

A
$\frac{3}{2}$
B
$\frac{4}{9}$
C
$\frac{2}{3}$
D
$\frac{9}{4}$

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Waves and Sound

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Energy and Intensity of Waves

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Statement-$1$: Two longitudinal waves given by equations $y_1(x, t) = 2a \sin(\omega t - kx)$ and $y_2(x, t) = a \sin(2\omega t - 2kx)$ will have equal intensity.
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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:

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$A$ stationary point source of sound emits sound uniformly in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $4 \ m$ and $9 \ m$ respectively from the source. The ratio of amplitudes of the waves at $P$ and $Q$ is

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$A$ 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

$A$ travelling wave is partly reflected and partly transmitted from a rigid boundary. Let $a_i, a_r$ and $a_t$ be the amplitudes of the incident wave,reflected wave,and transmitted wave,and $I_i, I_r$ and $I_t$ be the corresponding intensities. Choose the correct alternative.

The intensity of sound from a radio at a distance of $2 \ m$ from its speaker is $1 \times 10^{-2} \ \mu W/m^2$. The intensity at a distance of $10 \ m$ would be:

Statement-$1$: Two longitudinal waves given by equations $y_1(x, t) = 2a \sin(\omega t - kx)$ and $y_2(x, t) = a \sin(2\omega t - 2kx)$ will have equal intensity.Statement-$2$: Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.

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:

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Statement-$1$: Two longitudinal waves given by equations $y_1(x, t) = 2a \sin(\omega t - kx)$ and $y_2(x, t) = a \sin(2\omega t - 2kx)$ will have equal intensity.
Statement-$2$: Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.