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)