Can tape using different Media set ??

Here is my situation:

- Job 1 & 2 assigned to backup to same tape

- Job 1: Media set 1 (daily backup at 8pm)

- Job 2: Media set 2 (daily backup at 11pm)

- Media set 1 and 2 (overwrite protection period = 1 week, Infinite - Allow append)

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Job 1 succeed to backup but Job 2 failed ....

Is this beacuse tape after job 1 completed was assigned to "Media set 1", that made "Medis set 2" job can't start ??

Thanks