Final answer:
The shortest length of a pipe, open at both ends, to resonate at 256 Hz with a sound speed of 343 m/s is 0.670 meters, which is option (a).
Step-by-step explanation:
To find the shortest length of a pipe, open at both ends, which will resonate at a fundamental frequency of 256 Hz with the speed of sound being 343 m/s, we need to apply the formula for the fundamental frequency of an open pipe:
L = v / (2f)
Where L is the length of the pipe, v is the speed of sound, and f is the frequency.
Inserting the given values into the formula:
L = 343 m/s / (2 × 256 Hz)
= 343 m/s / 512 Hz
After calculating the value, we find:
L = 0.670 m
Therefore, the shortest length of the pipe resonating at 256 Hz is 0.670 meters, which corresponds to option (a).