12) A 10Hz P-wave traveling at 5km/s propagates for 1000m through a rock formation with an absorption coefficient of 0.2 dB/λ (that means it loses 0.2 dB per wavelength traveled by wave). What is the wave attenuation in decibel due solely to absorption? If the initial amplitude A0 =1, what is the final Amplitude?
Solution:
Amplitude loss (or) gain
in $dB=20\log_{10}\left(\frac{A_1}{A_2}\right) ---(1)$
Given that,
absorption coefficient $x=0.4
dB/\lambda$
Substitute
the x value in the above equation (1)
$0.4=20\log_{10}\left(\frac{1}{A_2}\right)$
$\frac{0.4}{20}=\log_{10}\left(\frac{1}{A_2}\right)$
$0.02=\log_{10}\left(\frac{1}{A_2}\right)$
$\frac{1}{A_2}=10^{0.02}$
$\frac{1}{A_2}=1.047$
$A_2=\frac{1}{1.047}$
$A_2=0.9547$
Therefore,
the final amplitude is $A_2=0.9547$
Post a Comment
Post a Comment