The scientific analysis of a Mantra is given below, as to how it attracts power when chanted by someone.

Everything has a particularvibratory frequency. Every thought, every word and every emotion. How we feel,think and speak defines our particular vibration. And we create our world basedupon that vibration. Sound is an incredibly powerfulvibration. Mana meansmind, “tra” means wave or projections. Thereforemantra is the projection of the mind through soundvibrations.
The basic structure of theuniverse is the atom, and the basic structure of our bodies is the cell; eachcell is made of billions of atoms and each atom is made of a positive nucleus and negative electrons rotating around it; because of this rotation, an electromagnetic field is generated similar to fields generated by an engine.
Every single atom is vibrating in a specific frequency, whether this atom is part of metal, water, cell, or anything else. So every thing in this universe is vibrating, this is a given scientific fact.
A small pebble thrown in a pond creates numerous ripples reaching quite far, in the same pond itself. Same way, the words, which we pronounce, creates vibrations and waves in our mind, which awaken subtle powers in us. Thus the Effects of whatever Words we speak, falls on our self, our society, and even on the universe…
Realizing this fact,that SOUND is the most powerful element; our ancientsages developed the science of Music or Sound (SHABDA) Therapy, called Bio-wavesor “Mantra” and a collection of Mantras called a “STOTRA”, which beingrelated to Ether (which is very subtle), becomes very powerful as the power ofSUBTLE (SUKSHAMA) is greater than the GROSS (STHOOLA). When atoms are isolated,it creates great energy & become more powerful, although it is so small thatit is impossible to see it, with our naked eyes, likewise when a person focuseson every single syllable and letter emanating from the Shabda Brahma (Mantra) orthe nada (the vibration) it is said to have profound effects on the psyche aswell as one’s physical self.

Mantra or Stotras are thosescientifically made sound combinations that affect our subtle Nerves – “SHATCHAKRAS” and “POWER CENTRES” directly in such a way, that it awakens our’powers’, which otherwise lie dormant. As a result these Nerves become activeand the person chanting is blessed with different powers(SIDDHI). In fact, (STOTRA SADHANA) isnothing else, but the Power of Sound. These Sanskrit Mantra letters contain bothEmotions and Meanings. The permutation and combinations of these letters havethe power to create wonders.
Sound being the base of the Mantra,makes it very powerful.

“When a Mantra is pronounced repeatedly, like a dynamo the Sound waves are transformed into electrical energy or vibrations & if coupled with deep emotions, becomes more powerful. These vibrations are in the shape of a Ring which rises up with great speed, through the medium of Ether, moving directly towards the presiding Deity of that Mantra. When it reaches its Deity, it combines with the power of that Deity before bouncing back along with the subtle but now manifold powers of that Deity back to re-enter the source of its origin which is the subtle body of the one chanting the Mantra. The Stronger the Faith, Will-power and Emotion attached with the Mantra, the Stronger will be the attraction of the powers of the Deity. It’s like a Dynamo effect, the more who keep repeating a Mantra continuously the more you get charged up with Divinity .This phenomenon is so subtle & so fast that the person chanting the Mantra does not even realize it as these sound waves or vibrations moving in the air in about 340m/sec have their own frequency while humans can hear only from 20 frequencies per second to20000 frequencies per second & not outside of this range.”

On the physically level the science of Sound works with the movement of the tongue in the mouth. The hard upper palate forms the roof of the mouth where there are 84 meridian points located. While pronouncing the Mantra, the movement of the tongue stimulates these meridian points which in turn stimulate the hypothalamus to secrete neurotransmission fluids. As these different chemical liquids are secreted to different parts of the brain, messages are transmitted throughout as well. Simultaneously, these Mantra sound vibrations are also received by the ear & are turned into electrical signals which move along the acoustic nerve towards the acoustic bark in the Brain, whose cells then correspond to these waves and move into the various parts of the brain especially the frontal part. All these parts work together corresponding to the signals and translating them to a language the human understands. And as, as our body is made up of at least 70 per cent water, our bodies become an excellent conductor of sound vibrations thus every cell in our body acts as a sound resonator. So finally, the brain analyses these signals and gives orders to the various parts of the body to correspond to these signals.
The signs of this charged Mantra, re-entering the subtle body of the person chanting it, are in the different types of Vibrations or Emotions that can move one to tears, lift his spirits up, bring back beautiful memories, make him deliriously happy, or rouse violent emotions, sensations of energy flowing from the head to the base or goose bumps too.
The mantra may be chanted out aloud, or repeated silently, or resonated in the mind (Japa) and should be recited from the base of the stomach which represents the seat of aperson’s dormant power. There is a lot of hidden shakti here. It produces subtle vibrations in the fine nerves of the brain, thereby empowering the brain’s 108 centers and quelling their inactivity.
If Mantras are pronounce dcorrectly, following the rules and regulations, given in the Scriptures it can undoubtedly cure many a diseases. So, the Success of the Mantra lies in its correct pronunciation. Unless the pronunciation is correct, it does not have the desirable effects on our Nerves.
JAPA and DHYANA, are similar to NAADA (Sound) and BINDUSAADHANA (Concentration on a point), which can pierce the great eror the subtlest particle.

The “Gayatri Mantra”GAYATRI MANTRA when repeatedly chanted, creates ring shaped sound waves which rises up with great speed, through Ether and goes to wards the Sun, and after touching the surface of the SUN, it returns back along with the subtle powers of the Sun, like Heat, Light, Electrical etc. Thus the Mantra combined with all these powers of the Sun re-enters the subtle body of the one chanting it. Who, therefore is regarded blessed by Gayatri Mata.
POWER OF MANTRA Tansen the famous court-musician of Emperor Akbar, could make the clouds pour down by singing the Raga MEGH MALHAAR, and could lit the lamps by singing RAGA DEEPAK.
POWER OF SOUND VIBRATIONS Two scientists by the name of GRAHAM and NEIL did a experiment in a crowded street, in Australia’s Melbournecity. The experiment was done to show the ‘POWERS OF SOUND’. The medium of the experiment was a Motor-Car. They wanted to move the car, according to their commands. The car followed their command when they said ‘START’ and again when they commanded ‘GO’, the car started moving and stopped when they said ‘HALT’. People thought it to be a magic, which in reality, it was not. It was merely an experiment, which showed the ‘Power of Sound’. But how did it happen?
Graham had a Transmitter in his hands; the function of the Transmitter was to convert the command into a fixed frequency of electrical power, and send it to the control unit, which was fitted in the dashboard of the car. Another device named ‘CAR RADIO’ was fitted in front of the Control-unit.
When the electro-magnetic frequencies transmitted by the Transmitter, dashed against ‘CAR RADIO’ the cars engine started and even began to move, and ultimately stopped. The source of all these happenings was the ‘SOUND WAVES’. The causes and effects of the ‘MANTRAS’ and ‘STOTRAS’ could not be analyzed till date, because they are based on Ultrasonic Sounds, which, we can neither see, nor hear. But if these are pronounced with clarity and emotion, than it can do wonders.