Final answer:
To calculate the frequency of the sound source in unison with an open-end and a closed-end organ pipe, we apply the harmonics relationship for open and closed pipes detecting that the sound source frequency is approximately 1134 Hz rounded to the nearest provided option.
Step-by-step explanation:
The student's question concerns calculating the frequency of a sound source that is in unison with both an open-end and a closed-end organ pipe, which are sounding their first overtone. Given that sound travels at 340 m/s, we need to find the frequency of both pipes and ensure they match since they are in unison.
For an open-end organ pipe, the first overtone is the second harmonic, which means the pipe length is equal to one wavelength. Using the formula f = v / λ, where f is the frequency, v is the speed of sound, and λ is the wavelength (twice the length of the open pipe), we can find the frequency. In the case of the closed-end organ pipe, the first overtone is the third harmonic, which makes the pipe ⅔ the wavelength long. Again, using the same formula and accounting for the third harmonic, we determine the frequency.
For the open pipe (30.0 cm), the frequency f_open = v / (2 * L) = 340 m/s / (2 * 0.3 m) = 567 Hz. For the closed pipe (23.0 cm), the frequency f_closed = v / (4 * L) since it is a third harmonic and the pipe is closed at one end. That is 340 m/s / (4 * 0.23 m) = 369 Hz.
However, as the pipes are in unison and the question states that they are resonating at their first overtone, the frequency given for the closed pipe must be the third harmonic or the first overtone of the open pipe being the second harmonic, hence we calculate the first overtone for the open pipe of 30.0 cm, which would be approximately 1134 Hz (567 Hz * 2). This corresponds to option (b) 1134 Hz, which must be rounded according to the available options.