An acoustic wave pulse is generated simultaneously at one end of a solid metal bar of length \(L\). The pulse propagates through the metal bar at speed \(v_m\) and through the surrounding air at speed \(v_a\), where \(v_m > v_a\). A detector at the far end of the bar measures a time delay \(\Delta t\) between the arrivals of the two pulses. Which of the following expressions correctly gives the length \(L\) of the metal bar in terms of \(\Delta t\), \(v_m\), and \(v_a\)?