Interrupts

So the project wasn't really "URGENT" after all ...

Have you already got working code that generates the sine wave that you want? Let's imagine it is in a function called makeSound()

Now all you need is code in loop() like this

void loop() {
   moveServo();
   makeSound();
   recordSound();
}

Or maybe like this

void loop() {
   moveServo();
   startRecord();
   makeSound();
   stopRecord();
}

...R