A resonator has natural frequency \(256\,\mathrm{Hz}\). At what driving frequency is the strongest simple resonance expected?

A resonance peak is centered at \(500\,\mathrm{Hz}\) with width \(25\,\mathrm{Hz}\). Find the quality factor \(Q\).

A resonator has \(Q=40\) and resonance frequency \(800\,\mathrm{Hz}\). Estimate the resonance width \(\Delta f\).

A closed tube resonates at its fundamental at \(170\,\mathrm{Hz}\). Use \(v=340\,\mathrm{m\,s^{-1}}\) to estimate its length.

An open-open tube of length \(0.50\,\mathrm{m}\) is driven by a speaker. Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the first three resonant frequencies.

An open-closed tube of length \(0.50\,\mathrm{m}\) is driven by a speaker. Use \(v=340\,\mathrm{m\,s^{-1}}\) to find the first three resonant frequencies.

A resonance has \(f_0=1000\,\mathrm{Hz}\) and \(Q=25\). Find \(\Delta f\).

A flute-like open-open air column is shortened from \(0.60\,\mathrm{m}\) to \(0.40\,\mathrm{m}\). By what factor does its fundamental frequency change?

The speed of sound in a pipe increases by \(3\%\) when the air warms. By what approximate percentage do all ideal resonant frequencies change if the pipe length is fixed?

A resonance peak narrows while its center frequency remains fixed. Does \(Q\) increase, decrease, or stay the same?

An open-closed tube of adjustable length resonates at \(440\,\mathrm{Hz}\) in its fundamental. Find its length for \(v=343\,\mathrm{m\,s^{-1}}\).

An open-open pipe of length \(0.75\,\mathrm{m}\) resonates near \(686\,\mathrm{Hz}\). Determine the mode number using \(v=343\,\mathrm{m\,s^{-1}}\).

A resonator has \(f_0=600\,\mathrm{Hz}\). Resonance remains strong from about \(588\,\mathrm{Hz}\) to \(612\,\mathrm{Hz}\). Estimate \(Q\).

A pipe has resonant frequencies \(150\,\mathrm{Hz}\), \(450\,\mathrm{Hz}\), and \(750\,\mathrm{Hz}\). Decide whether it behaves more like an open-open or open-closed resonator.

An open-open pipe is driven at fixed frequency \(f\). Derive the lengths \(L_n\) that resonate for mode number \(n\).

An open-closed pipe is driven at fixed frequency \(f\). Derive the lengths \(L_n\) that resonate for allowed mode number \(n\).

A resonance tube closed at one end shows adjacent resonances in length at \(0.18\,\mathrm{m}\) and \(0.52\,\mathrm{m}\) for the same tuning fork. Derive the wavelength and sound speed if the fork frequency is \(500\,\mathrm{Hz}\).

Two resonators have the same center frequency, but \(Q_A=20\) and \(Q_B=80\). Compare their bandwidths and explain which is more selective.

A pipe's resonant frequencies are proportional to sound speed. Using \(v\propto\sqrt{T}\), derive the fractional frequency change for a small temperature change \(\Delta T\ll T\).

A measured pipe spectrum contains \(f_1\), \(2f_1\), \(3f_1\), and weak non-harmonic peaks. Explain which peaks belong to the ideal air-column resonance model and give two physical reasons extra peaks might appear.