A medium has bulk modulus \(1.4\times10^5\,\mathrm{Pa}\) and density \(1.2\,\mathrm{kg\,m^{-3}}\). Estimate the sound speed.

A gas has \(\gamma=1.40\), pressure \(1.01\times10^5\,\mathrm{Pa}\), and density \(1.20\,\mathrm{kg\,m^{-3}}\). Find the sound speed.

If sound travels at \(340\,\mathrm{m\,s^{-1}}\), how far does it travel in \(0.25\,\mathrm{s}\)?

A sound echo returns from a wall after \(0.60\,\mathrm{s}\). If the sound speed is \(340\,\mathrm{m\,s^{-1}}\), find the one-way distance to the wall.

A liquid has \(B=2.2\times10^9\,\mathrm{Pa}\) and \(\rho=1000\,\mathrm{kg\,m^{-3}}\). Estimate the sound speed.

A material carries sound at \(1500\,\mathrm{m\,s^{-1}}\) and has density \(1000\,\mathrm{kg\,m^{-3}}\). Estimate its bulk modulus.

Two media have the same bulk modulus, but medium A has four times the density of medium B. Find \(v_A/v_B\).

Two gases have the same \(\gamma\) and molar mass. Gas 2 is at four times the absolute temperature of gas 1. Find \(v_2/v_1\).

A sound pulse travels \(510\,\mathrm{m}\) in \(1.5\,\mathrm{s}\). Find the sound speed and compare it with \(340\,\mathrm{m\,s^{-1}}\).

A thunderclap is heard \(4.0\,\mathrm{s}\) after lightning is seen. Estimate the distance to the lightning using \(v=340\,\mathrm{m\,s^{-1}}\).

For an ideal gas, use \(v=\sqrt{\gamma RT/M}\) to find the sound speed in air at \(T=300\,\mathrm{K}\), with \(\gamma=1.40\), \(R=8.31\,\mathrm{J\,mol^{-1}K^{-1}}\), and \(M=0.029\,\mathrm{kg\,mol^{-1}}\).

Air sound speed is \(331\,\mathrm{m\,s^{-1}}\) at \(273\,\mathrm{K}\). Use the ideal-gas scaling \(v\propto\sqrt{T}\) to estimate the speed at \(293\,\mathrm{K}\).

A sound pulse travels through \(20\,\mathrm{m}\) of air at \(340\,\mathrm{m\,s^{-1}}\) and then \(20\,\mathrm{m}\) of water at \(1480\,\mathrm{m\,s^{-1}}\). Find the total travel time.

Medium A has \(B_A=4B_B\) and \(\rho_A=\rho_B\). Compare the sound speeds and interpret the role of stiffness.

A gas's pressure and density are both doubled while \(\gamma\) stays fixed. Use \(v=\sqrt{\gamma p/\rho}\) to determine whether the sound speed changes.

Two ideal gases at the same temperature have the same \(\gamma\), but gas A has molar mass \(M_A\) and gas B has \(M_B=4M_A\). Derive \(v_A/v_B\).

Derive the units of \(\sqrt{B/\rho}\) and show that the expression has units of speed. Use \(1\,\mathrm{Pa}=1\,\mathrm{kg\,m^{-1}s^{-2}}\).

A fluid has unknown density. Its bulk modulus is \(2.0\times10^9\,\mathrm{Pa}\), and sound travels \(750\,\mathrm{m}\) through it in \(0.50\,\mathrm{s}\). Determine the density implied by the elastic-medium model and state one modeling assumption.

For an ideal gas, derive \(v=\sqrt{\gamma RT/M}\) from \(v=\sqrt{\gamma p/\rho}\) and the ideal-gas density relation \(\rho=pM/(RT)\). Interpret why pressure cancels at fixed temperature.

A gas changes from state 1 to state 2 with the same composition and \(\gamma\). Its pressure ratio is \(p_2/p_1=a\) and density ratio is \(\rho_2/\rho_1=b\). Derive \(v_2/v_1\), then state the condition for the sound speed to increase.