Question

Is 155dB ultrasound in the range of intensities used for deep heating? Calculate the intensity of this ultrasound and compare this intensity with the values quoted in the text.

Short answer

Yes, you can use 155dB ultrasound for deep heating.

Step-by-step solution

Formula for sound intensity level in dB (decibels)

The sound intensity level (SIL) or sound intensity level is the level (logarithmic quantity) of sound intensity relative to a reference value.

Now change this sound intensity level (dB) \[W \cdot {m^{ - 2}}\] by using the following formula.\[\beta = 10{\log _{10}}\left( {\frac{I}{{{I_0}}}} \right)\]

Here, \[\beta \] is the sound intensity level in dB, I is the intensity (in \[W \cdot {m^{ - 2}}\]) of ultrasound wave and \[{I_0}\] is the threshold intensity of hearing.

Intensity for 155dB ultrasound

Consider the given data as below.

Sound intensity level is,

\[\beta = 155{\rm{ }}dB\]

Threshold intensity of hearing is,

\[{I_0} = {10^{ - 12}}{\rm{ }}W \cdot {m^{ - 2}}\]

Calculate the intensity \[I\] for \[\beta = 155{\rm{ }}dB\] by using following formula.

\[\beta = 10{\log _{10}}\left( {\frac{I}{{{I_0}}}} \right)\]

\begin{aligned}\frac{\beta }{{10}} &= {\log _{10}}\left( {\frac{I}{{{I_0}}}} \right)\\\frac{\beta }{{10}} &= {\log _{10}}\left( {\frac{I}{{{I_0}}}} \right)\\\frac{I}{{{I_0}}} &= {\left( {10}\right)^{\frac{\beta }{{10}}}}\end{aligned}

Now replace \[_0\] and \[\beta \] with the given data.

\begin{aligned}I &= {10^{ - 12}}{\left( {10} \right)^{\frac{{155}}{{10}}}}\\ &= {10^{ - 12}}{\left( {10}\right)^{15.5}}\\ &= {10^{3.5}}\end{aligned}

The final value of intensity

\[I = 3.16 \times {10^3}{\rm{ }}W \cdot {m^{ - 2}}\]

Conclusion

The range of intensities used for deep heating is,

\[{10^3}{\rm{ }}W \cdot {m^{ - 2}} - {10^4}{\rm{ }}W \cdot {m^{ - 2}}\]

Our value of intensity \[I = 3.16 \times {10^3}{\rm{ }}W \cdot {m^{ - 2}}\] lies between this range so it can be used for deep healing.