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Because of bursty high data rate and delay sensitive nature of high quality multimedia application, the resource allocation in wireless network to meet its quality of service (QoS) has become the most challenging and interesting issue. Orthogonal Frequency Division Multiple Access (OFDMA) employing adaptive channel allocation technique can support these requirement while increasing the system capacity many fold. Here, an efficient resource allocation method called two stage rate adaptive (TSRA) algorithm is proposed in order to meet dynamic bandwidth requirement in downlink. We model the resource allocation problem with goal of maximizing spectral efficiency. Considering random mix of four categories of multimedia traffic, we find that gap between analytical and simulated average capacity of the system gets smaller as number of user increases and at one point the simulated average system capacity exceeds 6 b/s per Hz. Further, other system parameters like average throughput, delay and BER of the TSRA protocol is presented.