To determine the fundamental frequency at which a pipe resonates when it is open at both ends and is 40 centimeters long, we can use the following steps:
1. The fundamental frequency (f) for a pipe open at both ends can be calculated using the formula: f = v / (2L), where v is the speed of sound in air (approximately 343 m/s at room temperature) and L is the length of the pipe.
2. Convert the length of the pipe from centimeters to meters to be consistent with the speed of sound in air, which is usually given in meters per second. In this case, 40 centimeters is equal to 0.4 meters.
3. Substitute the values into the formula: f = 343 / (2 * 0.4).
f = 343 / 0.8
f = 428.75 Hz
Therefore, the pipe would resonate at the fundamental frequency of approximately 428.75 Hz when it is open at both ends and has a length of 40 centimeters.
