Standing Sound waves HELP?

Question

Find the fundamental frequency and the frequency of the first three overtones of a pipe 45 cm long

a) if the pipe is open at both ends
b) if the pipe is closed at one end. Use v=344m/s
c) For each of the above cases, what is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20Hz to 20,000 Hz

Answer 1

a) If the pipe is open at both ends, the fundamental wavelength is 2*45cm = 90cm. If v = 344m/s, the fundamental frequency is: (344m/s)/(0.90m) = 382. Hz.
The frequencies of the first three overtones are: 764. Hz, 1.15 kHz, and 1.53 kHz.

b) if the pipe is closed at one end, the fundamental wavelength is 4*45cm = 180cm. If v = 344m/s, the fundamental frequency is: (344m/s)/(1.80m) = 191. Hz.
The frequencies of the first three overtones are: 382. Hz, 573 Hz, and 764 Hz.

c) If the pipe is open at both ends, the fundamental frequency is: 382. Hz. Since 20000/382 >= 52, the 51st overtone will be heard.
If the pipe is open at one end, the fundamental frequency is: 191. Hz. Since 20000/191 >= 104, the 103rd overtone will be heard.