I will try to describe the utility of mantra and how it works. Though Sai, has already suggested a very good resource to understand Mantras.
Mantra : I will not discuss the definition. A Mantra is not what is written on a scripture, though Sanskrit being a versatile language to give most close assumption of how a word should sound. Any word on earth has significant important values like pitch,frequency,volume,echo, taal and many other factors. A mantra is a complete combination of all these, not only words or as they are written in the scriptures.
Mantra Siddhi : This is important to understand to clear your question. A Mantra Siddhi is recognition or remembrance of all the values of sound required for a mantra to work perfectly. It is like remembering a song and reproducing it as close as possible( that's why songs are given so importance in path of spirituality in Hinduism ).
Example : Om Yum Namah, mostly suggested to cure meager cancers. Here we know we have to start the Mantra with Om, but we don't know how long each word is to be said, and at what pitch or frequency, and or what combinations of sur and taal are required for the Mantra. We will bluntly read the Mantra as it is. Though reading it thousands of time, there will be situations where we would be close to the actual nature of Mantra and by time we might heal the cancer too, but that would not be quick.
Though a person who gains Siddhi, as learned at what pitch,frequency, sur and taal the mantra would work best, and the person with Siddhi when performs this mantra the result would be much quicker as expected, may be at an instant depending upon the level of Sidhhi he sought.
Are all mantras only for mental change ? All Mantras work on sound energy, none of the Mantra is sought through reading, all Mantras are mandatory to recite, as sound energy is involved in a Mantra, Mantras are mostly for Physical and Spiritual change only, though mental health depends on physical behavior of body and spiritual integrity of mind thus mental change is influenced accordingly.
Summing Up :Whether a Mantra will be quick or take time, depends on two factors, the nature of Mantra and the Nature of the person who's reciting it. A person with a Siddhi for a particular Mantra will make a Mantra's response much faster than a person without it. And a Mantra which is made slow in response will always react slowly for the Siddhi gained human, but will be enormously slow for a normal person.
Every sound that we make is actually a composite of sounds — a fundamental frequency and geometric multiples of that sound, called harmonics or overtones. Harmonics can also improve our vocal quality, charge our brain, improve our hearing and heighten our consciousness.
It can balance the left and right hemispheres of the brain, as well as the auric field. “Om” as you know, is said to be the original, primordial tone of the universe—the original sound of creation. More here
The effects of sound on the brain have been demonstrated in Electro Encephala Graph (EEG) charts as well as by documented physical changes (skin temperature, heart rate, respiratory rate among them).
Beeja, or Bija mantras can be very helpful in balancing the brain hemispheres as well as the chakra system. Refer
The chanting improves your voice by giving strength to your vocal
cords and the muscles around it. This is very helpful during old age.
The vibrations of Om open up the sinuses to clear the airways. The
sound uuu… (U) is created by the vocal cords which benefit the thyroid
glands and the throat. Read it
Suggestion: Some day just relax, sit alone in a room and chant AUM with eyes closed, feel as if it is originating from root chakra (muldhara) and moving upwards. Feel the difference, within and outside.
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