(B) The energy $E$ of a sound wave is proportional to the square of its amplitude $A$ and the square of its frequency $n$. Mathematically,$E \propto A

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(B) The energy $E$ of a sound wave is proportional to the square of its amplitude $A$ and the square of its frequency $n$. Mathematically,$E \propto A^2 n^2$.Since the energies of the waves produced by $P$ and $Q$ are equal,we have $E_P = E_Q$.This implies $A_P^2 n_P^2 = A_Q^2 n_Q^2$.Given $n_P = n$ and $n_Q = \frac{n}{4}$,we substitute these values into the equation:$A_P^2 n^2 = A_Q^2 (\frac{n}{4})^2$.$A_P^2 n^2 = A_Q^2 (\frac{n^2}{16})$.Dividing both sides by $n^2$,we get $A_P^2 = \frac{A_Q^2}{16}$.$A_Q^2 = 16 A_P^2$.Taking the square root of both sides,we get $A_Q = 4 A_P$.

Class 11 Physics Waves and Sound Energy and Intensity of Waves

Medium

$A$ musical instrument $P$ produces sound waves of frequency $n$ and amplitude $A_P$. Another musical instrument $Q$ produces sound waves of frequency $\frac{n}{4}$. The waves produced by $P$ and $Q$ have equal energies. If the amplitude of waves produced by $P$ is $A_P$,the amplitude of waves produced by $Q$ will be: (in $A_P$)

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A
$2$
B
$4$
C
$6$
D
$8$

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Class 11

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Chapter

Waves and Sound

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Energy and Intensity of Waves

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$A$ transverse wave is passing through a stretched string with a speed of $20 \ m/s$. The tension in the string is $20 \ N$. At a certain point $P$ on the string,it is observed that energy is being transferred at a rate of $40 \ mW$ at a given instant. Find the speed of point $P$.

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The intensity of a sound wave while passing through an elastic medium falls by $10\%$ as it covers $1 \ m$ distance through the medium. If the initial intensity of the sound wave was $100 \ dB$,its value after it has passed through $3 \ m$ thickness of the medium will be .... $dB$.

Medium

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Which of the following statements is correct?

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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

DifficultKCET 2009

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The sound intensity level at a point $4 \,m$ from the point source is $10 \,dB$. Then the sound level at a distance $2 \,m$ from the same source will be ........ $dB$.

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$A$ transverse wave is passing through a stretched string with a speed of $20 \ m/s$. The tension in the string is $20 \ N$. At a certain point $P$ on the string,it is observed that energy is being transferred at a rate of $40 \ mW$ at a given instant. Find the speed of point $P$.

The intensity of a sound wave while passing through an elastic medium falls by $10\%$ as it covers $1 \ m$ distance through the medium. If the initial intensity of the sound wave was $100 \ dB$,its value after it has passed through $3 \ m$ thickness of the medium will be .... $dB$.

Which of the following statements is correct?

$A$ 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

The sound intensity level at a point $4 \,m$ from the point source is $10 \,dB$. Then the sound level at a distance $2 \,m$ from the same source will be ........ $dB$.

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