The sound level of the ultrasound used in medical diagnostics is approximately 108.72 dB.
To find the sound level in decibels (dB) for a given power intensity, you can use the formula:
dB = 10 * log10(I/I0)
where I is the given power intensity and I0 is the reference intensity.
In this case, the power intensity is 7.47 * 10^(-2) W/m^2. However, we need to know the reference intensity to calculate the sound level in dB. The reference intensity typically used for sound level measurements is 1 * 10^(-12) W/m^2.
Substituting the values into the formula:
dB = 10 * log10(7.47 * 10^(-2) / (1 * 10^(-12)))
Simplifying:
dB = 10 * log10(7.47 * 10^10)
Using the properties of logarithms:
dB = 10 * (log10(7.47) + log10(10^10))
dB = 10 * (log10(7.47) + 10)
Calculating the logarithm and multiplying:
dB = 10 * (0.872 + 10)
dB = 10 * 10.872
dB ≈ 108.72
Therefore, the sound level of the ultrasound used in medical diagnostics is approximately 108.72 dB.