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Unformatted text preview: First ask yourself when will the ant feel weightless?....when going up with acceleration or going down with some acceleration.Solution lies in going down with acceleration because this acceleration of going down will oppose the g. Therefore the ant should go down with acceleration "g" so that it ffels weightless" Now suppose the sinusoidal wave created by the man by tapping his foot is given by: Now double differentiate it wrt t so that you get the acceleration at which the rope particles go up and down: Now we know a=g , for ant to feel weight less. Therefore, Now for A to be minimum ,sinwt=1 Therefore you get Now for the value of "w" , we need the wavelength. Now velocity of the sinusoidal wave is given by: where m= mass per unit length Now apply v=f (lamda) Calculate frequency from above formula Now w= 2(pie)f Decibels cost distance Put the value in above equation to get the answer... As I have difficulty editing equations in your Word file, I am writing the answers here, and using "b" instead of "beta", "log10" to say "log with base 10", etc The definition of the difference in decibels between two intensities f1 and f2 is b2 = b1+ 10*log10(f2/f1) There seems to be some confusion with the formula at the top of your page (possibly caused by the same causes that do not let me edit the equations). In any case the formula I have written here is the definition Answer to question A: If the intensity increased by factor f = f2/f1, then the new level of sound is b2 = b1+ 10*log10(f) Answer to question B: The intensity is inversly proportional to the square of the distance, that is f2/f1 = d1^2/d2^2 therefore, if the listener moved from distance d1 to distance d2, the change in the level of sound is delta b = 10*log10(f2/f1) = 10*log10(d1^2/d2^2) = 20*log10(d1/d2) So this is your answer to B: delta b = 20*log10(d1/d2) ...
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- Spring '09