Learn Turkish: Bağırmak zorundayız çünkü müzik çok yüksek. - We have to shout because the music is very loud.

We use the infinitive verb bağırmak (to shout) followed by zorundayız. The word zorunda indicates obligation or necessity, and we add the personal ending -ız (we are) with a buffer -y- in between because zorunda ends in a vowel. Together, bağırmak zorundayız expresses the external obligation "we have to shout".

Why does yüksek mean "loud" here? Doesn't it usually mean "high"?

Yes, yüksek literally means "high". However, in Turkish, volume is described in terms of level or height rather than "loudness". When talking about sound, "loud music" or a "loud voice" naturally translates to yüksek müzik or yüksek ses.

Could I use gerekiyor (it is necessary) instead of zorundayız to express the same thing?

You could say bağırmamız gerekiyor (our shouting is necessary), but zorundayız is a stronger fit for this context. Zorunda emphasizes a strict external obligation or lack of choice: you have absolutely no option but to shout because the environment (the loud music) is forcing you to.