Two adjacent natural frequencies of an organ pipe are found to be 900 Hz and 990 Hz.

(a) Calculate the fundamental frequency and length of this pipe.

other info that I already calculated:
-the pipe is open at both ends
- length of pipe is 1.89m

To calculate the fundamental frequency and length of the organ pipe, we can make use of the relationship between the length of the pipe and its resonant frequencies.

The fundamental frequency (also known as the first harmonic) is the lowest frequency at which the pipe vibrates. For a pipe open at both ends, the fundamental frequency can be calculated using the formula:

f1 = v / (2L)

Where:
f1 = fundamental frequency
v = speed of sound in air (approximately 343 m/s at room temperature)
L = length of the pipe

From the given frequencies, we can determine that the fundamental frequency (f1) is 900 Hz. Using the equation above, we can rearrange it to solve for L:

L = v / (2f1)

Substituting the known values:

L = 343 m/s / (2 * 900 Hz)
L ≈ 0.1906 m

Therefore, the length of the organ pipe is approximately 0.1906 meters or 1.906 cm.

Note: It's important to emphasize that the calculated length is different from the one provided (1.89m). Please double-check your calculations or re-evaluate the given information, as a discrepancy may exist.