Answer
64.8k+ views
Hint: The amount of energy passing per unit time through a unit area that is perpendicular to the direction in which the sound waves are travelling is known as the sound intensity. Sound intensity can be calculated in units of energy or work.
Useful formula:
The formula for intensity of the sound is;
$I = \dfrac{P}{{4\pi {r^2}}}\,\,$
Where, $I$ denotes the intensity of the sound of the bird, $P$ denotes the power of the intensity of the sound.
Complete step by step solution:
The data given in the problem are;
The intensity of the sound is $10\,\,db$.
Let the initial position be at a ${r_1}$ distance from the bird and the final position ${r_2}$ distance from the bird.
The formula for intensity of the sound is;
${I_1} = \dfrac{P}{{4\pi r_1^2}}\,\,,\,\,{I_2} = \dfrac{P}{{4\pi r_2^2}}$
Where, ${I_1}$ denotes the intensity of the sound at the first distance, ${I_1}$ denotes the intensity of the sound at the sound distance, $P$ denotes the power of the intensity of the sound.
In the decibel form substitute the values given data;
$10\,\,\log \dfrac{{{I_2}}}{{{I_o}}} - 10\,\,\log \dfrac{{{I_1}}}{{{I_o}}} = 10$
Where, ${I_o}$ denotes the total intensity of the sound.
$
10\,\,\log \dfrac{{{I_2}}}{{{I_o}}} - 10\,\,\log \dfrac{{{I_1}}}{{{I_o}}} = 10 \\
\log \,\,\dfrac{{{I_2}}}{{{I_1}}} = 1 \\
\dfrac{{r_1^2}}{{r_2^2}} = 10 \\
{r_1}:{r_2} = \sqrt {10} :1 \\
$
Note: Sound intensity which can also be the acoustic intensity, which can be explained as the power loaded by sound waves per unit area in a side perpendicular to that area. Sound intensity is not the same physical quantity as sound pressure. Human hearing is directly sensitive to sound pressure which is related to sound intensity.
Useful formula:
The formula for intensity of the sound is;
$I = \dfrac{P}{{4\pi {r^2}}}\,\,$
Where, $I$ denotes the intensity of the sound of the bird, $P$ denotes the power of the intensity of the sound.
Complete step by step solution:
The data given in the problem are;
The intensity of the sound is $10\,\,db$.
Let the initial position be at a ${r_1}$ distance from the bird and the final position ${r_2}$ distance from the bird.
The formula for intensity of the sound is;
${I_1} = \dfrac{P}{{4\pi r_1^2}}\,\,,\,\,{I_2} = \dfrac{P}{{4\pi r_2^2}}$
Where, ${I_1}$ denotes the intensity of the sound at the first distance, ${I_1}$ denotes the intensity of the sound at the sound distance, $P$ denotes the power of the intensity of the sound.
In the decibel form substitute the values given data;
$10\,\,\log \dfrac{{{I_2}}}{{{I_o}}} - 10\,\,\log \dfrac{{{I_1}}}{{{I_o}}} = 10$
Where, ${I_o}$ denotes the total intensity of the sound.
$
10\,\,\log \dfrac{{{I_2}}}{{{I_o}}} - 10\,\,\log \dfrac{{{I_1}}}{{{I_o}}} = 10 \\
\log \,\,\dfrac{{{I_2}}}{{{I_1}}} = 1 \\
\dfrac{{r_1^2}}{{r_2^2}} = 10 \\
{r_1}:{r_2} = \sqrt {10} :1 \\
$
Note: Sound intensity which can also be the acoustic intensity, which can be explained as the power loaded by sound waves per unit area in a side perpendicular to that area. Sound intensity is not the same physical quantity as sound pressure. Human hearing is directly sensitive to sound pressure which is related to sound intensity.
Recently Updated Pages
Write a composition in approximately 450 500 words class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Arrange the sentences P Q R between S1 and S5 such class 10 english JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What is the common property of the oxides CONO and class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
What happens when dilute hydrochloric acid is added class 10 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
If four points A63B 35C4 2 and Dx3x are given in such class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
The area of square inscribed in a circle of diameter class 10 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Other Pages
In the ground state an element has 13 electrons in class 11 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Excluding stoppages the speed of a bus is 54 kmph and class 11 maths JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Differentiate between homogeneous and heterogeneous class 12 chemistry JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Electric field due to uniformly charged sphere class 12 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
According to classical free electron theory A There class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
A boat takes 2 hours to go 8 km and come back to a class 11 physics JEE_Main
![arrow-right](/cdn/images/seo-templates/arrow-right.png)