This phrase has been a pet lines for my English teacher. I heard her saying this a number of times. The phrase likely originated from the observation that an empty container, like a barrel, makes a louder, more resonant sound when struck than a full one. But using this line into our daily life does make a sense. There is also a proverb in Hindi on this theme as -'थोथा चना बाजे घना '- Thotha chana baaje ghana i.e. hollow seeds of Gram produce more sound. Now i found the Sanskrit version of this and it says :
उत्तमो नातिवक्ता स्यात् मध्यमो बहु भाषते
न काञ्चन ध्वनिस्तादृक् यादृक् कांस्य प्रजायते.
Uttamo naativaktaa syaat madhyamo bahu bhashate,
Na kaanchan dhwanistaadruk yaadruk kaansya prajaayate.
Uttam = Best. (here reference is to honourable persons)
Naati vaktaa = (na + ati + vaktaa)
Na = not.
Ati = too much.
Vaktaa = 0ne who is speaking. Syaat = are.
Madhyam = middle .
Bahu = too much.
Bhaashate = speak, talk.
Kaanchan = gold.
Dhwani = sound .
Taadruk = like that of.
Yaadruk = like this.
Kansya = bronze , an alloy of tin and copper used for making bells, as it produces loud sound. compared to Gold, which produces only a thud, bronze (a base metal) produces a loud sound.
Prajayate = produces.
Honourable persons never indulge in loose talks whereas ordinary persons talk too much unnecessarily, just as Gold (considered as best and costliest metal) does not produce a loud sound like bronze ( a base metal) on being struck.
This phrases highlights that knowledgeable persons do not indulge in unnecessary and loose talk, whereas those who are less knowledgeable are always talkative. If someone is constantly interrupting a conversation and expressing opinions without any real understanding of the topic, they might be described as an "empty vessel making the most noise".
The proverb is often contrasted with the idea that "still waters run deep," implying that those who are knowledgeable and insightful may be more reserved and less prone to making a lot of noise.