Question

Deep ultrasonic heating is used to promote healing of torn tendons. It is produced by applying ultrasonic sound over the affected area of the body. The sound transducer (generator) is circular with a radius of 1.09 cm, and it produces a sound intensity of 6.86 × 103 W/m2. How much time is required for the transducer to emit 4040 J of sound energy?

Answer 1

Explanation:

It is given that,

Radius of sound transducer, r = 1.09 cm = 0.0109 m

Sound intensity, $I=6.86\times 10^3\ W/m^2$

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.

$I=\dfrac{P}{A}$

$I=\dfrac{P}{\pi r^2}$

$P=I\times \pi r^2$

Energy per unit time is called power i.e.

$P=\dfrac{E}{t}$

$t=\dfrac{E}{I\pi r^2}$

$t=\dfrac{4040\ J}{6.86\times 10^3\ W/m^2\times \pi (0.0109\ m)^2}$

t = 1577.80 seconds

So, 1577.80 seconds is required for the transducer to emit 4040 J of sound energy.