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A wave is a propagating disturbance that can transfer energy and information without requiring a net transport of matter over the same distance. Frequency, wavelength and propagation speed are linked; what oscillates locally depends on the kind of wave and its medium. Atomic emission and absorption spectra contain discrete lines because atoms exchange photons whose energies match differences between quantized energy states. Spectral lines provide a direct experimental bridge between quantum energy levels and the chemical identity of an element. Spectroscopy studies how matter emits, absorbs or scatters electromagnetic radiation as a function of wavelength, frequency or energy. Spectra act like structured fingerprints: their lines and bands reveal energy levels, composition and molecular structure.
Primary references
IUPAC Gold Book · NIST · BIPM