Transfering audio data between two DSP's, clock sync problem
If both DSPs cannot be slaved to the same oscillator for some reason you must use sample rate conversion. This is because after awhile, you inevitably will have 1 more or 1 fewer sample due to slightly mismatched clock rates. You can use simple interpolation, or more complex sinc based SRC methods for much better audio performance (see this paper for example). Alternatively, it is typically possible for the audio clock (for example, a I2S or AC97 clock) to be asynchronous from the DSP's internal processing clock, but this will largely depend on if the DSP has internal hardware to cross that clock domain (basically, it needs a dual clock FIFO). Some DSPs designed for audio (for example, the Analog Devices SHARC series) will have built in sample rate conversion modules for this exact purpose.