Final answer:
The organ pipe in question is open at both ends. The two harmonics are the first overtone and the third overtone. The length of the pipe can be determined using the formulas for wavelength and the harmonic number.
Step-by-step explanation:
(a) In this scenario, the organ pipe has two successive harmonics with frequencies of 1372 Hz and 1764 Hz. Since these harmonics are odd-numbered harmonics (1st and 3rd harmonics), it indicates that the pipe is open at both ends. In an open pipe, both ends are antinodes and the wavelength of the fundamental frequency is 2 times the length of the pipe.
(b) The first harmonic corresponds to the fundamental frequency, which is also called the first overtone. The second harmonic corresponds to the third overtone. So, the two harmonics in this case are the first overtone and the third overtone.
(c) To find the length of the pipe, we can use the formula:
Length of pipe = (n × wavelength) / 2
Where n is the harmonic number. For the first overtone (n = 1), the length of the pipe is equal to half the wavelength. For the third overtone (n = 3), the length of the pipe is equal to three halves of the wavelength.
Since the first overtone corresponds to a frequency of 1372 Hz, we can calculate the wavelength of the first overtone using the formula:
wavelength = speed of sound/frequency
By substituting the values into the formula, we get:
wavelength = 343 m/s / 1372 Hz = 0.25 m.
So, the length of the pipe for the first overtone is:
Length of pipe = (1 × 0.25 m) / 2 = 0.125 m