1.

Prove that DeltaL=10log_(10)[(I_(1))/(I_(0))] decibel, from Weber-Fechner's law.

Answer» <html><body><p></p>Solution :According to Weber-Fechner's law, ''loudness (L) is proportional to the logarithm of the actual intensity (I) measured with an accurate non-human instrument''. It is meant that <br/> `LproplnI` <br/> `L=klnI` <br/> The difference between two loudnesses, `L_(1)andL_(0)` <a href="https://interviewquestions.tuteehub.com/tag/measures-1091959" style="font-weight:bold;" target="_blank" title="Click to know more about MEASURES">MEASURES</a> the relative loudness between two precisely measured intensities and is called as sound intensity level. Mathematically, sound intensity level is <br/> `DeltaL=L_(1)-L_(0)=klnI_(1)-klnI_(0)` <br/> `=<a href="https://interviewquestions.tuteehub.com/tag/kln-1063084" style="font-weight:bold;" target="_blank" title="Click to know more about KLN">KLN</a>[(I_(1))/(I_(0))]` <br/> If k=1, then sound intensity level is measured in bel, in <a href="https://interviewquestions.tuteehub.com/tag/honour-487929" style="font-weight:bold;" target="_blank" title="Click to know more about HONOUR">HONOUR</a> of Alexander Graham Bell. <br/> `:.DeltaL=ln[(I_(1))/(I_(0))]`bel <br/> However, this is practically a bigger unit, so we use a convenient smaller unit, called <a href="https://interviewquestions.tuteehub.com/tag/decibel-435735" style="font-weight:bold;" target="_blank" title="Click to know more about DECIBEL">DECIBEL</a>. Thus, decibel `=(1)/(10)bel`. Hence, by multiplying and dividing by 10 we get <br/> `DeltaL=10(ln[(I_(1))/(I_(0))])(1)/(10)bel` <br/> `DeltaL=10ln[(I_(1))/(I_(0))]` decibel with k=10 <br/> For practical purposes, we use logarithm to base 10 instead of natural logarithm, <br/> `DeltaL=10log_(10)[(I_(1))/(I_(0))]` decibel.</body></html>


Discussion

No Comment Found

Related InterviewSolutions