(A) The energy of oscillations is given by the formula $E = \frac{1}{2} m \omega^2 A^2$. Since $\omega = 2 \pi n$,we have $E \propto n^2 A^2$. Given t

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(A) The energy of oscillations is given by the formula $E = \frac{1}{2} m \omega^2 A^2$. Since $\omega = 2 \pi n$,we have $E \propto n^2 A^2$. Given that the energies of the waves produced by $X$ and $Y$ are equal,we can write: $n_X^2 A_X^2 = n_Y^2 A_Y^2$. Substituting the given values $n_X = n$,$A_X = A$,and $n_Y = \frac{n}{3}$: $n^2 A^2 = (\frac{n}{3})^2 A_Y^2$. $n^2 A^2 = \frac{n^2}{9} A_Y^2$. $A^2 = \frac{A_Y^2}{9}$. $A_Y^2 = 9 A^2$. Taking the square root on both sides,we get $A_Y = 3 A$.

Class 11 Physics Waves Energy and Intensity of Waves

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$A$ musical instrument $X$ produces sound waves of frequency $n$ and amplitude $A$. Another musical instrument $Y$ produces sound waves of frequency $\frac{n}{3}$. The waves produced by $X$ and $Y$ have equal energies. The amplitude of waves produced by $Y$ will be (in $A$)

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$3$
B
$4$
C
$2$
D
$1$

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Waves

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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.
Statement-$2$: Intensity of waves of given frequency in the same medium is proportional to the square of amplitude only.

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Consider ten identical sources of sound,all emitting the same frequency but having random phase angles. If the average intensity of each source is $I_0$,what will be the average resultant intensity $I$ due to all these ten sources?

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There is a long linear source of sound whose power is $P$ and length is $L$. At point $A$,the sound level is $80 \ dB$. Then at point $B$,the sound level will be .... $dB$.

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The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure. The ratio of their intensities $I_A/I_B$ is equal to:

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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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$A$ musical instrument $X$ produces sound waves of frequency $n$ and amplitude $A$. Another musical instrument $Y$ produces sound waves of frequency $\frac{n}{3}$. The waves produced by $X$ and $Y$ have equal energies. The amplitude of waves produced by $Y$ will be (in $A$)

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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.

Consider ten identical sources of sound,all emitting the same frequency but having random phase angles. If the average intensity of each source is $I_0$,what will be the average resultant intensity $I$ due to all these ten sources?

There is a long linear source of sound whose power is $P$ and length is $L$. At point $A$,the sound level is $80 \ dB$. Then at point $B$,the sound level will be .... $dB$.

The displacement-time graphs for two sound waves $A$ and $B$ are shown in the figure. The ratio of their intensities $I_A/I_B$ is equal to:

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.