Achieving clean and quiet combustion in gas turbines is essential for improving many low-carbon energy and propulsion technologies. This often requires suppression of combustion instabilities and combustion generated noise in gas turbine combustors. Entropy noise is the less explored mechanism of combustion generated sound. Central to the emission of entropic sound is the survival of entropy wave during convection by the mean flow and reaching the combustor exit nozzle. Yet, the annihilation of entropy waves in this process is still poorly understood. To address this issue, the evolution of convected entropy waves in a fully-developed, cold flow inside a circular duct is investigated experimentally. Entropy waves are produced by a well-controlled electrical heater. Fast-response, miniaturized thermocouples arranged over a moveable cross-section of the duct are employed to record the state of entropy waves at different axial locations along the duct. Hydrodynamic parameters including Reynolds number and turbulence intensity are varied to investigate their effects upon the wave decay. The results show that the decay process is strongly wavelength dependent. It is found that the wave components with wavelengths larger than the duct diameter are almost unaffected by the flow and therefore remain essentially one-dimensional. However, other spectral components of the wave are subject to varying degrees of dissipation and loss of spatial correlation. Overall, the results support the recent numerical findings about the likelihood of wave survival in adiabatic flows. They further clarify the validity range of the one-dimensional assumption commonly made in the literature.