When the room temperature experiences a small variation from T to T + T , the fundamental frequency of an organ pipe shifts from to + . Which of the following expressions correctly relates the fractional change in frequency to the fractional change in temperature?

Step-by-step solution

The fundamental frequency of an organ pipe is given by = v , where v is the speed of sound and is the wavelength. The speed of sound in a gas at absolute temperature T is given by v = R T M . Thus, the fundamental frequency is directly proportional to the square root of the absolute temperature: T = k T^ 1/2 Taking the natural logarithm on both sides: = k + 1 2 T Differentiating both sides for small variations: = 1 2 T T