Why Pentecost? Why that day?

Why Pentecost? Why did the Spirit come on the church on that day in particular?

It's a good question. Jesus ascended on a Thursday; the Spirit did not come for another 10 days. Why the wait? Jesus only said that they'd have to wait for "a few days", but 10 is longer than it might have been.

Perhaps it was just expedient. There would be multi-national crowds in Jerusalem over the Pentecost festival, making it a perfect time for them to hear the wonders of God in their own tongues.

Maybe.

David Gooding, in his book True to the Faith, offers another suggestion. This is from page 33 in my edition, but it looks like it may have been replubished in an expanded form (so your page number may be different). I rather like it:

“Pentecost was originally one of a pair of agricultural festivals, celebrating the beginning of the first harvest of the year. Before the standing corn was completely ripe and ready, a sheaf was cut and offered as firstfruits to God (Lev. 23:9-11). Fifty days later (that is, on the day of Pentecost), two loaves baked from the first flour to be milled from the newly reaped grain were also offered as firstfruits to God (Lev. 23:15-17). Harvest time in any primitive economy is always a joyous occasion. In Israel the joy was both natural and sacred. Cod, they believed, had given them Canaan as their inheritance; harvest was the reaping of the blessings of that God-given inheritance. Later in the year there would come other harvests, of grapes and other fruits; and they would be celebrated in other festivals. But there was nothing quite like the joy of these first two festivals, when the pinching scarcities and gloom of winter gave way to the glorious taste of the firstfruits of the year's first harvest.

“Israel had been celebrating these agricultural festivals for centuries. But the year Jesus rose from the grave there were bigger things to celebrate. His resurrection was the first break in a more terrible winter; his glorified body the firstfruits of a mightier harvest (1 Corinthians 15:23). Fifty days later, on the day of Pentecost, the Holy Spirit came as the firstfruits of a greater inheritance, a foretaste and guarantee of creation’s final restoration (Romans 8:18-23; 2 Corinthians 5:1-5; Ephesians 1:13-14). The freshness and joy of it pervade Luke’s history still.”