Pipe A is an open organ pipe of length 0.50m. Pipe B is another open pipe whose length can be varied. At 30∘C (speed of sound v=349ms−1), the third harmonic of pipe B beats with the fourth harmonic of pipe A producing 4 beats per second.
(i) Calculate the fundamental frequency of pipe A.
(ii) Determine the frequency of the fourth harmonic of pipe A.
(iii) Using the given beat frequency information, find the two possible values of the fundamental frequency of pipe B and hence its corresponding possible lengths.
(iv) State with reason which of the two lengths is physically more likely if the pipes are nearly in unison when sounded together.