Yes, in general.
The PHB actually defines spell components:
A spell's components are the physical requirements you must meet in order to cast it. Each spell's description indicates whether it requires verbal (V), somatic (S), or material (M) components.
It later identifies somatic components as "spellcasting gestures".
Burning hands specifies a physical act that must be performed to cast the spell. This fits the definition of a spell component, and it's a hand gesture rather than a spoken word or a material object, so it is a somatic component.
Same for dissonant whispers, except that the act is chanting or singing the discordant melody, so it's a verbal component.
Gray area: suggestion, command, etc.
Spells that require you to speak what you want the spell to do are tricky. Consider command: "You speak a one-word command to a creature you can see within range." I would read that as a verbal component, since you are required to speak the command for the spell to work. On the other hand, verbal components are described as "mystic words", implying that they're not an ordinary word like "Kneel!" used with command. On the other other hand, that sentence starts with "Most spells", leaving open the possibility that some spells require speaking normal words instead of, or in addition to, the mystic words. (Vicious mockery, for example, clearly requires speaking words with both mundane and arcane meaning: "a string of insults laced with subtle enchantments".)
There's been much discussion over whether these spells require "mystic words" to be spoken, especially in the case of suggestion, where it's really not in your interest to signal that you're casting a spell. But that's a separate issue.
The real question is, why does it matter whether the mundane words are a verbal component? You have to say them anyway. I suppose someone might argue that they can use Subtle Spell to cast command without saying the word out loud, but that's a question for the DM to settle when it happens.
Gray area: spells that make weapon attacks (green-flame blade, etc.)
Since the weapon attack is a physical act that makes the spell work, it is a component, and green-flame blade lists "weapon" as a material component, but claims not to have a somatic component. That seems correct: you have to do something with the weapon, but attacking is not a "gesture" as such. Instead, the attack should be treated as a special kind of component separate from the usual V/S/M categories.
However, again, what difference does it make? Even if it was a somatic component, nobody's going to cast a Subtle green-flame blade where they don't attack anyone. That's the whole point of the spell. Similarly, if a magic item enables you to cast the spell without components, it would need to specify how you attack without the required weapon (most likely the magic item itself would be the weapon). It's hard to see a case where it matters.