We use diffusing-wave spectroscopy to measure the motion of droplets i
n concentrated emulsions subjected to a periodic shear strain. The str
ain gives rise to periodic echoes in the correlation function which de
cay with increasing strain amplitude. For a given strain amplitude, th
e decay of the echoes implies that a finite fraction of the emulsion d
roplets never rearranges under periodic strain while the remaining fra
ction of droplets repeatedly rearranges. Yielding occurs when about 4-
5% of the droplets rearrange.