Question

When an organist practices in an unheated church in January the temperature is at 3 oC, but when the organ was originally tuned, the temperature was 29 oC. What percent change does this cause in the "speaking frequency" of most of the pipes? (Do not enter the percent sign, just the number. If the tone goes down enter a negative number. If it is unchanged, enter 0. For example, if you think the new frequency will be 14 percent lower than when it was tuned, enter the number -14.)

Answer 1

The organ pipe produces sounds of a particular wavelength and the wavelength doesn't change with temperature, whereas speed of the sound changes.

f = ν/λ, frequency is proportional to the speed of the sound if the wavelength is constant.

The organ's original tuning was always done at 9^oC above room temperature, so the sound speed was

v_o = v = 344 m/s + ((0.6 m/s ^oC)x9^oC) = 349 m/s

The new temperature is 26^oC below room temperature, so the new sound speed is

v_n = v = 344 m/s + ((0.6 m/s ^oC)x26^oC) = 359.6 m/s

percentage change = $\small \frac{v_n-v_o}{v_n}\times100=\frac{359.6-349}{359.6}\times100=+2.78\%$

The percent change cause in the speaking frequency of most of the pipes is +2.78%