A turbomachine turbine assembly having a longitudinal axis and including an exhaust casing, an ejection cone arranged downstream of the exhaust casing, the ejection cone having an outer annular wall for the flow of a primary air stream and an acoustic box arranged radially inside said outer annular wall. The acoustic box can include a radially inner annular wall and a connection member interposed longitudinally between the exhaust casing and the inner annular wall of the ejection cone. The connection member can be fastened to the exhaust casing and to the inner annular wall. The upstream end of the outer annular wall can be connected to the connection member with a degree of freedom in the radial direction and a degree of freedom in the longitudinal direction.