The angular distributions of multiquantum excitations of the lowest energy, frustrated translational vibrations of a low coverage of CO chemisorbed on Cu(001) have been investigated by high resolution helium scattering time-of-flight measurements. The elastic and the one-phonon creation and annihilation cross sections show several interference undulations as a function of parallel momentum transfer, and up to four multiquantum overtones. All the experimental observations are in reasonable agreement with a multiquantum scattering theory, which also provides information on the height and width of the adsorbed CO molecules. PACS numbers: 82.65. My, 79.20.Rf, 82.65.Pa Important information on the structure and dynamics of adsorbates on surfaces comes primarily from spectroscopic studies of the frequencies of the vibrational modes, whereas information on energy exchange and deexcitation comes from the linewidths [1,2]. The higher vibrational frequencies of chemisorbed molecules are usually measured by infrared absorption [1,2] or by electron energy loss spectroscopy (EELS) [3] whereas for the low frequency vibrations helium atom scattering (HAS) has established itself as an ideal experimental probe [4 -6].Carbon monoxide adsorbed on ordered crystal surfaces has probably been studied more than any other adsorbate system [7]. At the on-top position it exhibits two high frequency modes for the molecule-surface stretch (v2 mode) and the C-0 stretch (v~mode) with energies of several 100 meV, an intermediate frequency mode attributed to the frustrated rotational motion (v3) with an energy less than 100 meV, and a very low frequency mode associated with frustrated translational motion (v4, designated vT in the present paper) of the molecule with an energy often less than 10 meV. This lowest frequency mode, which has been measured with both HAS [4 -6] and recently EELS [8,9] on a variety of surfaces, is important for a number of reasons. Because of its small energy it is the major contributor to the mean square vibrational amplitude of the CO molecule and the vibrational entropy [10]. Moreover, it is an important source of information on the lateral CO-surface potential [11],and because of its low frequency provides an efficient energy transfer pathway for the deexcitation of the internal C-0 stretch and CO-surface stretch modes to the phonons of the substrate [12]. The phonon dispersion curves of the clean Cu(001) surface have recently been intensively studied by HAS [13] and preliminary HAS results for the frustrated translation mode for CO on Cu(001) were also recently published [14].In the present study we report on a detailed HAS investigation of the excitation of the frustrated translational mode as a function of parallel momentum transfer in the very low coverage regime where the CO adsorbate molecules are isolated on on-top sites with the C atom closest to the surface. At small parallel momentum transfer tiQ (close to specular scattering conditions) the HAS time-of-flight (TOF) spectra exhibit only single-phonon clear...