A cylinder with a diameter of 11.1 cm is filled with water to some height. The air-filled part of the cylinder acts as a tube with one closed end and one open end. The air has a density of 1.10 kg/m³ and a bulk modulus of 1.33 × 10^5 Pa.
Part A: What is the speed of sound?
Part B: If the cylinder is sounded at its third harmonic with a frequency of 255.7 Hz, what is the depth of the column of air?
Part C: After adding some water, the cylinder still resonates at 255.7 Hz, but at no lower frequency. What is the volume of water that needs to be added? (in m³)
A string fixed at both ends is placed near the open end of the cylinder. The length of the string is 1.3 m and its mass is 8.5 g. When the cylinder is sounded at the third harmonic frequency (as in Part B), the string is in resonance at the second overtone.
Part D: What is the wave speed on the string?
Part E: What is the tension in the string?