Final answer:
The fundamental frequency of a 32.0 cm piccolo, when the speed of sound is 343 m/s, can be calculated using the formula f = v / (2L) and is approximately 537 Hz. The closest given option is B) 533 Hz.
Step-by-step explanation:
The question is asking to determine the fundamental frequency of a piccolo given its length and the speed of sound in air. A tube that is open at both ends, such as a piccolo, will have a fundamental frequency that is determined by the wavelength of the sound wave that fits exactly twice in the length of the tube. The formula for the fundamental frequency (f) is given by f = v / (2L), where v is the speed of sound in the medium (343 m/s, in this case) and L is the length of the tube.
To find the fundamental frequency of the piccolo, we would use the length L = 32.0 cm = 0.32 m. Plugging these values into the formula, we calculate the frequency: f = 343 m/s / (2 × 0.32 m) = 536.875 Hz, which is approximately 537 Hz. Since we do not have an option that exactly matches this value, we choose the closest option, which in this case is B) 533 Hz.