Rabbi Roodyn

ד) הָרִיעוּ לַה’ כָּל הָאָרֶץ פִּצְחוּ וְרַנְּנוּ וְזַמֵּרוּ

Shout to the Lord, all the earth, open [your mouths] and sing praises and play music.

The Malbim explains that when a king is ensconced in his palace people sing in his honour and play on the harp and other string instruments. But when he leaves his palace to be among his people they shout out in joy.

Since our pasuk is talking about Hashem’s salvation, it is as if He has come out of His palace, this elicits a jubilant response from all of humanity as they perceive His actions and attributes.  Or as Rav Hirsch puts it, the events of Jewish History and the wondrous acts that Hashem has performed on our behalf will call on the inhabitants of the world to wake up and pay homage to Hashem. The term פצחו, means that they will not restrain the joyous emotions that are stirred up their hearts by what they have witnessed. These emotions will be expressed fully through the medium of joyous song.