Q4. A pipe 50 cm long is closed at one end. Taking v = 340 m s, find the frequency of its second overtone (the third possible mode).
The modes are odd harmonics of v/4L = 340/2.0 = 170 Hz: 170, 510, 850 Hz, … The third mode, the second overtone, is the fifth harmonic: 850 Hz.
Q5. Two pipes have the same length; one is open at both ends and the other closed at one end. What is the ratio of their fundamental frequencies?
Open: v/2L; closed: v/4L. Open : closed = 2 : 1.
Q6. The tension in a string fixed at both ends is made four times larger. What happens to its fundamental frequency?
ν1 = v/2L and v = √(T/μ) ∝ √T, so the fundamental frequency doubles.