What type of vocal exercises should I be looking for?
Are there any temporary influences to the vocal range, like having had a drink?
If what you want is to improve your vocal range, I would recommend these exercises:
Finally, remember to take into account your physical limitations. You might be able to widen up your vocal range a bit, but there's always going to be a limit. Good luck!
Always warm up in the middle of your range and gradually approach the limits of your range with upward and downward moving repetition of motifs.
e.g. C3 D3 E3 D3 C3--- | D3 E3 F3 E3 D3--- | E3 F3 G3 F3 E3--- | and so on...
Even a single warm up with ascending and descending exercises will temporarily increase your range for a time.
Exercises that cross vocal registers are also helpful (and arguably even more important)
Which part of your voice do you want to expand on?
It really depends, as each register is different. For example, are you looking to work on fry, chest, head or whistle?
There are different techniques for each register, and the thing is, everyone has a huge vocal range, no matter what voice type, tessitura they have as their vocal instrument. Honestly, everyone has around 4-5 octaves of range at least if you use the right techniques.
If you are looking to do vocal fry, it’s really the sound you make when you wake up, “grunt” then get out to bed. It’s the grunting sound you make, so pretty much everyone has it. It can be a bit uncontrollable at times. If you are looking on how to control fry, the key element required is really time. Like whistles, they may take years to perfect.
As for chest voice (the register you use when you speak, for lower notes) use the exercises / techniques mentioned above amounts. For example, sing C4-D4-E4-F4-G4 , G5-A5-B5-A5-G5 etc.
Head voice - Try mixing (it’s quite an advanced technique though) and control it by using your diaphragm muscles. Remember, don’t strain too much as vocal damage can be easily done here,
Whistle - This register is by far the hardest to perfect out of the few mentioned above. All women have the “whistle” element in their voice, but in men they are replaced as falsetto. Whistles don’t take much power, but they are difficult to truly grasp. Think of it as super head voice. I don’t have anymore advice on this, if you want to know about the whistle element google it.
It takes time to expand. Be patient.
Similar to humming, another type of practice that makes you comfortable while singing is praticing akaras, eekaras, oookaras, like you sing aa...a....in akaara practice, eeee....eeeeee in eekara and ooo....oooo.... in oookara practice. As all languages cover the words with these or any one of these syllable or sound, this enables singing all kinds of langauge in the world. This has worked out the best for me.