To solve this question, we need to follow several steps related to fundamental principles of physics, specifically the speed of sound in air and the frequency of vibrations in open and closed pipes.
The first step is to understand the speed of sound in air at a certain temperature. At a temperature T (in this case T=20°C), the speed of sound in air (v), is estimated using the formula:
v = 331.3 * sqrt(1 + T / 273.15)
The number 331.3 represents the speed of sound in meters per second at 0 degree Celsius. The temperature, T, needs to be converted to Kelvin, hence we divide it by 273.15. Adding 1 to the ratio and taking the square root gives us the actual speed of sound at the given temperature.
The second step is to calculate the frequency (f) for an open pipe. The frequency for an open pipe is determined using the formula:
f_open = v / (2 * L)
where v is the speed of sound calculated earlier, and L is the length of the pipe, in this case, L = 0.54m.
The third step is to calculate the frequency (f) for a closed pipe. The frequency for a closed pipe is obtained using the formula:
f_closed = v / (4 * L)
where, again, v is the speed of sound and L is the length of the pipe.
According to the calculations performed based on the given conditions, the open pipe has a frequency of approximately 317.79 Hz and the closed pipe has a frequency of approximately 158.90 Hz.