Explanation:
It is given that,
Radius of sound transducer, r = 1.09 cm = 0.0109 m
Sound intensity, [tex]I=6.86\times 10^3\ W/m^2[/tex]
Sound energy, E = 4040 J
We need to find the time required to emit 4040 J of sound energy. We know that intensity is given by power per unit area i.e.
[tex]I=\dfrac{P}{A}[/tex]
[tex]I=\dfrac{P}{\pi r^2}[/tex]
[tex]P=I\times \pi r^2[/tex]
Energy per unit time is called power i.e.
[tex]P=\dfrac{E}{t}[/tex]
[tex]t=\dfrac{E}{I\pi r^2}[/tex]
[tex]t=\dfrac{4040\ J}{6.86\times 10^3\ W/m^2\times \pi (0.0109\ m)^2}[/tex]
t = 1577.80 seconds
So, 1577.80 seconds is required for the transducer to emit 4040 J of sound energy.
