A soda bottle with some water inside can be used as a musical instrument. To tune it properly, the fundamental frequency must be 440.0 Hz. The sound speed (v) is 343 m/s. Treat the bottle as a pipe that is closed at one end and open at the other end.
(a) Is this sound wave transverse or longitudinal? Explain why.
(b) Treat the above bottle as a pipe of length of L with only one open end, what are the wave lengths when the condition for resonance (standing wave) is satisfied?
(c) If the bottle is H = 26.0 cm tall, how high h should it be filled with water to produce the fundamental mode (the first harmonic) of the desired frequency?
(d) What is the frequency of the next harmonic for this bottle?