FA20 CREW ON AN ARR TO YIP LEVEL AT FL240 WERE CHANGED TO AN INCORRECT FREQ DELAYING THEIR DSCNT ON THE ARR.

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WE WERE LEVEL AT FL240 ON THE CRUXX 4 ARR INTO YIP AND JUST HANDED OFF TO NEW CTR FREQ. BOTH THE FO AND I THOUGHT WE HEARD THE CTLR ACKNOWLEDGED US CHKING IN ON FREQ. THIS NEW FREQ WAS VERY CONGESTED AND THE CTLR WAS VERY BUSY. WE WERE EXPECTING TO GET A LOWER ALT SOON. ABOUT 25 MI PRIOR TO CRUXX INTXN; I TRIED TO REQUEST LOWER ALT FROM CTR TO MEET THE XING ALT TO 'EXPECT' AT CRUXX. IT WAS VERY DIFFICULT TO GET THROUGH TO CTR. FINALLY HE HEARD US AND AFTER A BRIEF PAUSE; THE CTLR TOLD US TO GO BACK TO OUR LAST ASSIGNED FREQ. WE WERE NOT IN HIS SECTOR. AS WE WERE DOING THAT; DETROIT APCH WAS CALLING US ON 121.50. WE GOT ON THE CORRECT FREQ AND THEN DSNDED AND SEQUENCED INTO THEIR AIRSPACE FOR OUR ARR TO YIP. THERE WERE NO OTHER PROBS WITH THE FLT. IN CONCLUSION. SOMEHOW THERE WAS A MISCOM ON OUR INITIAL CONTACT WITH CTR. WHEN WE WERE NOT BEING ASSIGNED LOWER ALTS AS EXPECTED FOR THE ARR; I STARTED CALLING CTR BUT FREQ CONGESTION DELAYED THIS. BY THAT TIME; WE WERE OUT OF HIS SECTOR AND HAD TO RE-ESTABLISH COM WITH A CTLR. ALL THESE DELAYS CAUSED US TO CROSS CRUXX AT FL240.