This research work proposes a new method for performing sample selection in audio steganographic systems, which can also be applied to strictly frequency-based and spatial steganographic systems. This method exploits the predictability of pseudo-random number generators to generate a sequence of pseudo-random indices to develop a steganographic system that offers security without compromising the payload capacity of the carrier signal. A comparative study has also been performed among existing sample selection algorithms, namely, sequential selection and pseudo-random selection with indices embedded within the stego object. Our analysis also looks at the effect of applying RSA encryption on the source message having the stego object created. For this study, the source messages are both grayscale and RGB image files. The carrier file used is a 32-bit stereo WAV file. The metrics chosen to perform the comparative study include PSNR, Mean Square Error, Normalized Absolute Error, and Structural Content. To judge the resilience of the steganographic systems from a security point of view, the histogram analysis method is utilized to perform steganalysis. Further, the ineffectiveness of encryption in the steganographic process is also analyzed. The proposed method overcomes the vulnerabilities inherent to sequential and random sample selection methods using the unique sample selection method devised in this paper.