The unusual HMSFR Orion Becklin-Neuberger (Orion BN/KL) at the heart of the Orion Molecular Cloud-1 (OMC-1) is examined, with its associated explosive outflow of gas and dust. Its four well-studied features are the Hot Core, Compact Ridge, Plateau, and Extended Ridge. These sources offer much evidence for the sequential chemical processing of shocked molecular cloud material and indicate just how violent the dynamic processes associated with HMSFRs can be.

Comparisons between low- and high-flux PDR conditions are discussed in relation to the Horsehead Nebula and the Orion Bar. Contrasting observations of selected species between the PDR margin and the inner dark cloud allow chemical modellers to test formation and destruction reaction networks against quite closely constrained physical conditions. The anomalous abundance of CH3CN is considered here in the Horsehead context in the presence of other nitrile COMs observed, as are comparisons of sulphur chemistry in the low- and high-flux cases and the latest ideas on the ISM sulphur reservoir.

The chapter takes a detailed look at low-mass star formation towards IRAS 16293-2422, a warm core surrounding a binary source within the L1689 cloud of Ophiuchus. Prestellar cores are strung out in elongated filamentary structures of dense gas and dust. Sensitive temperature measurements distinguish prestellar cores from unbound starless cores. Towards the Class 0 protostar source in IRAS 16293 detailed views of the principal components associated with low-mass star formation are discussed, from dense cloud filaments to rotating accretion disk, bipolar outflows, and larger circumbinary envelopes. IRAS 16293 shows warm/hot corino chemistry (warm carbon chain chemistry, WCCC), illustrating the conditions in which the chemical signatures involving COMs help us to define the structure of disks and envelopes on scales of ~100-1,000 AU. Both COMs and deuterated species, particularly the ratios of deuterated species to their hydrgenated counterparts, trace gas and dust temperatures and densities, and compositionally dependent gas–grain interactions, through comparisons with chemical modelling.

The ATLASGAL PDR survey is discussed with its high detection rates of chosen PDR tracers towards HII sources. While previous chemical modelling of specific sources shows that in a cold lower-density envelope the abundances of C2H and c-C3H2 vary little, subsequently during cloud collapse (with density increase, temperature rise, and the emergence of HII regions) from 105 yr on in the models the column density ratio increases steeply. The observed abundances of some high-column-density tracers (H13CO+ and HC15N) in the survey are almost constant over the range of H2 column densities, while others (HCO, CN, C2H and c-C3H2) fall as H2 increases. The HCO detections are confirmed as arising from clumps likely associated with PDRs, and higher HCO abundances are undoubtedly linked in the models to ongoing FUV chemistry.

The chapter presents two surveys of low-mass star formation regions (LMSFR). The first survey uses the IRAM (Institute for Radio Astronomy in the Millimeter Range) 30 metre telescope at Pico Veleta in Spain to identify 16 deeply embedded YSOs and the emission from eight complex organic molecules (COMs). The second survey uses ALMA (Atacama Large Millimetre Array) directed towards five low-mass candidates (all in the Serpens cluster at distances ~440 pc) and detected emission from five COMs species.

Wave solutions of short duration, or transients, are shown to be equivalent to the sum of a large number of sinusoidal solutions over a range of frequencies. The range of frequencies is inversely proportional to the time duration. This result can be expressed mathematically as an uncertainty principle and explains why waves of very short duration do not have an identifiable pitch. A similar phenomenon occurs during a rapid rise or fall of a signal. Spectrographs can be used to represent a changing spectrum as a function of time, where data are collected and analyzed with a moving time window, similar to what appears to happen for human perception. In contrast to periodic signals, for a short transient signal, the phase factors in the Fourier series are most important for perception.

The basics of sound propagation in three dimensions are considered. Simple models for sources are presented, including isotropic and nonisotropic sources, such as the dipole, quadruple, line sources, and oscillating baffles. Sound propagation from those sources is treated in the ray approximation, where effects due to the wave nature of sound are suppressed. For finite sources, it is shown that in the absence of reflections, sound intensity falls off following an inverse square law. Reflections in a room are considered and lead to reverberation. The time sound remains in a room is characterized using a reverberation time, and a simple equation is used to relate that time to room dimensions, materials used, and possible contents of the room. Sound in a room from multiple sources is considered using sound-energy density rather than intensity. One example of the treatment of multiple sources is known as the cocktail party effect.

The results for the vibrating string are generalized to discuss vibrating systems that are not necessarily harmonic. Solutions are characterized by counting the nodes for solutions—that is, locations where the vibrational amplitude is always zero. One-dimensional solutions for uniform bars and rods, relevant for various chimes and bars used for music, are presented. The nonuniform bars used for xylophones and marimbas, and how they are used for tuning, are presented. The procedure is generalized for two-dimensional objects, where node lines are considered, and applied to membranes, such as drum heads, and plates. The complications that arise with degeneracies, or multiple solutions with the same frequency, are presented. A general, symbolic way of representing vibrational modes is shown, as well as how that can, very symbolically, represent any possible solution for a vibrating object as a sum of those with sinusoidal time dependence.