A sound wave in air has frequency \(680\,\mathrm{Hz}\) and speed \(340\,\mathrm{m\,s^{-1}}\). Find its wavelength.

A sound wave has wavelength \(0.85\,\mathrm{m}\) and speed \(340\,\mathrm{m\,s^{-1}}\). Find its frequency.

A sound wave has frequency \(250\,\mathrm{Hz}\). Find its period.

State whether sound in air is longitudinal or transverse, and describe the direction of air-particle motion relative to propagation.

At one point in a sound wave, the equilibrium pressure is \(1.01\times10^5\,\mathrm{Pa}\) and the pressure variation is \(+24\,\mathrm{Pa}\). Find the instantaneous pressure and identify compression or rarefaction.

At one point in a sound wave, \(\Delta p=-18\,\mathrm{Pa}\). Is that point in a compression or a rarefaction?

A sinusoidal sound wave has \(k=12\,\mathrm{rad\,m^{-1}}\) and \(\omega=4080\,\mathrm{rad\,s^{-1}}\). Find its wave speed.

A sound wave has wavelength \(0.50\,\mathrm{m}\). Find its wavenumber \(k\).

A sound wave has frequency \(440\,\mathrm{Hz}\). Find its angular frequency.

For \(\xi(x,t)=\xi_0\cos(kx-\omega t)\), determine the direction of propagation and explain the sign choice.

A sound wave is described by \(\xi(x,t)=2.0\times10^{-6}\cos(5.0x-1700t)\), with SI units. Find the displacement amplitude, wavelength, frequency, and direction of travel.

A microphone records pressure variation \(\Delta p(t)=12\sin(2\pi(500)t)\,\mathrm{Pa}\) at a fixed point. Find the pressure amplitude, frequency, and period.

A sound pulse travels \(170\,\mathrm{m}\) through air in \(0.50\,\mathrm{s}\). It then enters a different medium and travels \(900\,\mathrm{m}\) in \(2.0\,\mathrm{s}\). Find each sound speed and state which medium carries sound faster.

Two listeners are separated by \(68\,\mathrm{m}\) along the direction of propagation of a \(340\,\mathrm{m\,s^{-1}}\) sound wave. Find the time delay between when the same compression reaches them.

A wave has pressure variation \(\Delta p(x,t)=30\sin(4x-1360t)\,\mathrm{Pa}\). Find its speed and classify the pressure state at \(x=0\), \(t=0\).

A sinusoidal sound wave has particle displacement \(\xi=\xi_0\cos(kx-\omega t)\) and pressure variation \(\Delta p=\Delta p_{\max}\sin(kx-\omega t)\). At a position where the displacement is maximum positive, what is the pressure variation? Explain using phase.

A sound wave travels from air into another medium. Its frequency remains fixed at \(500\,\mathrm{Hz}\), while its speed changes from \(340\,\mathrm{m\,s^{-1}}\) to \(1500\,\mathrm{m\,s^{-1}}\). Derive the wavelength change and interpret why frequency is not changed by entering the new medium.

A right-moving sound wave has constant phase \(kx-\omega t=C\). Derive the speed of a compression from this constant-phase condition and explain why this is not the speed of an individual air parcel.

A detector measures two pressure maxima at the same point separated by time \(\Delta t\), and two neighboring pressure maxima in space separated by distance \(\Delta x\). Derive \(f\), \(\lambda\), and the sound speed from these measurements.

A sound wave and a transverse string wave have the same \(f\), \(\lambda\), and speed. Construct a comparison that identifies what is the same mathematically and what differs physically between the two wave models.