A-level Physics (Advancing Physics)/Standing Waves/Worked Solutions

'''1. The air in a 3m organ pipe is resonating at the fundamental frequency. Organ pipes are effectively open at both ends. What is the wavelength of the sound?'''

$$3 = \frac{\lambda}{2}$$

so λ = 2 x 3 = 6m.

'''2. A string is vibrating at the second harmonic frequency. How many wavelengths long is the standing wave created?'''

$$(2 + 1) \times \frac{\lambda}{2} = \frac{3\lambda}{2}$$

3. Express, in terms of λ, the length of a pipe which is closed at one end, where λ is the length of one wave at the fundamental frequency.

¼λ (this is the distance between a node and an antinode)