Problem 33P

(a) At T = 20°C, how long must an open organ pipe be to have a fundamental frequency of 294 Hz? (b) If this pipe is filled with helium, what is its fundamental frequency?

Solution 33PIntroductionAt first we have to supply energy to increase the temperature of the mercury to the boilingpoint. Then we have to supply energy to change its phase from liquid to vapor, which is thelatent heat of vaporization.SolutionStep 1The boiling point of mercury is 356.7°C. So first we have to increase the temperature from20°C to 356.7°C. The required energy is given byQ 1 mcTWhere m is the mass of mercury = 20 gc is the specific heat of mercury = 0.14 J/g/KAnd change in temperature T is = (356.7 20) = 336.7°C = 336.7 KSo the required energy Q i1 = (20 g)(0.14 J/g/K)(336.7 K) = 940 J