A physics student uses a water-filled vertical resonance tube (closed at the bottom by the water surface, open at the top) to estimate the speed of sound in the laboratory. She strikes a tuning fork of frequency 440Hz and slowly lowers the water level until she hears the first strong resonance at an air column length of 19.0cm. A standard end correction of 1.5cm is appropriate for the open end of the tube. Assume the air is dry and motionless.
(a) Derive an expression for the speed of sound in terms of the measured resonant length, the end correction, and the tuning-fork frequency. Clearly state the physical condition for the first resonance in a tube closed at one end.
(b) Calculate the speed of sound using the measured data.
(c) Using the empirical relation v=331m/s+0.60m/s×T(∘C), determine the laboratory air temperature implied by your result from part (b).
(d) A thermometer in the room reads 23∘C. Compute the percentage discrepancy between the temperature inferred from acoustics and the thermometer reading. Provide two plausible experimental or environmental factors that could account for the discrepancy.