  Cuprate superconductors host a multitude of low-energy optical phonons. Using
time- and angle-resolved photoemission spectroscopy, we study coherent phonons
in Bi$_{2}$Sr$_{2}$Ca$_{0.92}$Y$_{0.08}$Cu$_{2}$O$_{8+\delta}$. Sub-meV
modulations of the electronic band structure are observed at frequencies of
$3.94\pm 0.01$ and $5.59\pm 0.06$ THz. For the dominant mode at 3.94 THz, the
amplitude of the band energy oscillation weakly increases as a function of
momentum away from the node. Theoretical calculations allow identifying the
observed modes as CuO$_{2}$-derived $A_{1g}$ phonons. The Bi- and Sr-derived
$A_{1g}$ modes which dominate Raman spectra in the relevant frequency range are
absent in our measurements. This highlights the mode-selectivity for phonons
coupled to the near-Fermi-level electrons, which originate from CuO$_{2}$
planes and dictate thermodynamic properties.
