An open-open pipe has length \(0.85\,\mathrm{m}\). Use \(v=340\,\mathrm{m\,s^{-1}}\) to find its fundamental frequency.

An open-closed pipe has length \(0.85\,\mathrm{m}\). Use \(v=340\,\mathrm{m\,s^{-1}}\) to find its fundamental frequency.

At an open end of an ideal pipe, is the pressure variation a node or an antinode?

At a closed end of an ideal pipe, is the air-particle displacement a node or an antinode?

Find the first three frequencies of an open-open pipe of length \(1.0\,\mathrm{m}\), using \(v=340\,\mathrm{m\,s^{-1}}\).

Find the first three allowed frequencies of an open-closed pipe of length \(1.0\,\mathrm{m}\), using \(v=340\,\mathrm{m\,s^{-1}}\).

An open-open pipe has fundamental frequency \(220\,\mathrm{Hz}\). Find the frequency of its fourth harmonic.

An open-closed pipe has fundamental frequency \(120\,\mathrm{Hz}\). Which of \(240\,\mathrm{Hz}\), \(360\,\mathrm{Hz}\), and \(600\,\mathrm{Hz}\) are allowed ideal resonances?

An open-open pipe resonates at \(300\,\mathrm{Hz}\) in its fundamental. Find its length using \(v=340\,\mathrm{m\,s^{-1}}\).

An open-closed pipe resonates at \(250\,\mathrm{Hz}\) in its fundamental. Find its length using \(v=340\,\mathrm{m\,s^{-1}}\).

An open-open pipe has length \(0.60\,\mathrm{m}\). Find the wavelength and frequency of the \(n=3\) mode using \(v=340\,\mathrm{m\,s^{-1}}\).

An open-closed pipe has length \(0.60\,\mathrm{m}\). Find the wavelength and frequency of its third allowed mode \((n=3)\), using \(v=340\,\mathrm{m\,s^{-1}}\).

A pipe has resonances at \(170\,\mathrm{Hz}\), \(340\,\mathrm{Hz}\), and \(510\,\mathrm{Hz}\). Decide whether this pattern better matches open-open or open-closed behavior.

A pipe has resonances at \(90\,\mathrm{Hz}\), \(270\,\mathrm{Hz}\), and \(450\,\mathrm{Hz}\). Decide whether this pattern better matches open-open or open-closed behavior.

Derive the open-open allowed frequencies from the condition that \(n\) half-wavelengths fit into length \(L\).

Derive the open-closed allowed frequencies from the condition that an odd number of quarter-wavelengths fits into length \(L\).

A pipe of unknown end condition has consecutive resonances at \(510\,\mathrm{Hz}\) and \(680\,\mathrm{Hz}\). Use the spacing to find the fundamental spacing and give one possible pipe type and length for \(v=340\,\mathrm{m\,s^{-1}}\).

An open-open pipe and an open-closed pipe have the same length \(L\). Compare their fundamental frequencies and explain the geometry of the difference.

An ideal pipe has one end definitely open. Its allowed frequencies are \(f,3f,5f,\ldots\). Prove that the other end must behave as closed in the simple air-column model.

A pipe of length \(L\) has one end adjustable between effectively open and effectively closed. Explain how the fundamental wavelength changes between the two limits and derive the frequency ratio.