The Power of mantra chanting
Hare Krsna-Below we have arranged a series of quotes  starting with material sound vibrations which  have the power to circle the earth 7 times in one second . Going from there to spiritual vibrations which can penetrate the hearts and ears of all living entities and also travel all the way to the Vaikuntha planets in the spiritual sky. Also included is the process of how to chant these mantras as given by the bona fide spiritual master Srila Prabhupada

.Hare Krsna

damaghosa das—————————————

Aug 21 1973 london 
Just like electricity is everywhere, electrons. One who can tackle the electrons, they can talk without any direct connection by electronic method, thousand thousand miles away. Just like radio message, television message. So similarly, Kṛṣṇa is also everywhere. Just like the waves of sound wave is going on. As soon as you produce, I produce one sound, immediately within a second the sound goes round the earth seven times. So if a material thing has got so much power, just think how much power God has got. 
SB 1.8.13 purport
The brahmāstra, the supreme weapon released by Aśvatthāmā, was something similar to the nuclear weapon but with more radiation and heat. This brahmāstra is the product of a more subtle science, being the product of a finer sound, a mantra recorded in the Vedas. Another advantage of this weapon is that it is not blind like the nuclear weapon because it can be directed only to the target and nothing else. Aśvatthāmā released the weapon just to finish all the male members of Pāṇḍu’s family; therefore in one sense it was more dangerous than the atomic bombs because it could penetrate even the most protected place and would never miss the target.
Madhya 17.45-When the Lord loudly chanted “Hari bol!” the trees and creepers became jubilant to hear Him.
PURPORT-The loud chanting of the Hare Kṛṣṇa mantra is so powerful that it can even penetrate the ears of trees and creepers-what to speak of animals and human beings. Śrī Caitanya Mahāprabhu once asked Haridāsa Ṭhākura how trees and plants could be delivered, and Haridāsa Ṭhākura replied that the loud chanting of the Hare Kṛṣṇa mahā-mantra would benefit not only trees and plants but insects and all other living beings. One should therefore not be disturbed by the loud chanting of Hare Kṛṣṇa, for it is beneficial not only to the chanter but to everyone who gets an opportunity to hear.

SB 4.24.32 purportLord Śiva voluntarily came to bless the sons of the King as well as do something beneficial for them. He personally chanted the mantra so that the mantra would be more powerful, and he advised that the mantra be chanted by the King’s sons (rāja-putras). When a mantra is chanted by a great devotee, the mantra becomes more powerful. Although the Hare Kṛṣṇa mahā-mantra is powerful in itself, a disciple upon initiation receives the mantra from his spiritual master, for when the mantra is chanted by the spiritual master, it becomes more powerful. Lord Śiva advised the sons of the King to hear him attentively, for inattentive hearing is offensive.
Adi lila 8.28-As a result of chanting the Hare Kṛṣṇa mahā-mantra, one makes such great advancement in spiritual life that simultaneously his material existence terminates and he receives love of Godhead. The holy name of Kṛṣṇa is so powerful that by chanting even one name, one very easily achieves these transcendental riches.

Adi lila 10.43 purport..Certainly the chanting of 300,000 holy names of the Lord is wonderful. No ordinary person can chant so many names, nor should one artificially imitate Haridāsa Ṭhākura’s behavior. It is essential, however, that everyone fulfill a specific vow to chant the Hare Kṛṣṇa mantra. Therefore we have prescribed in our Society that all our students must chant at least sixteen rounds daily. Such chanting must be offenseless in order to be of high quality. Mechanical chanting is not as powerful as chanting of the holy name without offenses.
SB 3.28.34 purport-Here it is clearly mentioned that meditation, which is an action of the mind, is not the perfect stage of samādhi, or absorption.In the beginning the mind is employed in attracting the form of the Supreme Personality of Godhead, but in the higher stages there is no question of using the mind.A devotee becomes accustomed to serving the Supreme Lord by purification of his senses. In other words, the yoga principles of meditation are required as long as one is not situated in pure devotional service. The mind is used to purify the senses, but when the senses are purified by meditation, there is no need to sit in a particular place and try to meditate upon the form of the Lord. One becomes so habituated that he automatically engages in the personal service of the Lord. When the mind forcibly is engaged upon the form of the Lord, this is called nirbīja-yoga, or lifeless yoga, for the yogī does not automatically engage in the personal service of the Lord. But when he is constantly thinking of the Lord, that is called sabīja-yoga, or living yoga. One has to be promoted to the platform of living yoga.One should engage in the service of the Lord twenty-four hours a day, as confirmed in the Brahma-saṁhitā. The stage of premāñjana-cchurita can be attained by developing complete love. When one’s love for the Supreme Personality of Godhead in devotional service is fully developed, one always sees the Lord, even without artificially meditating on His form. His vision is divine because he has no other engagement. At this stage of spiritual realization it is not necessary to engage the mind artificially. Since the meditation recommended in the lower stages is a means to come to the platform of devotional service, those already engaged in the transcendental loving service of the Lord are above such meditation. This stage of perfection is called Kṛṣṇa consciousness.Madhya 9 7-8- purport…The holy names of Kṛṣṇa and Hari, or the chanting of the Hare Kṛṣṇa mahā-mantra, are so spiritually powerful that even today, as our preachers go to remote parts of the world, people immediately begin chanting Hare Kṛṣṇa. Śrī Caitanya Mahāprabhu was the Supreme Personality of Godhead Himself. There cannot be anyone who can compare to Him or His potencies. However, because we are following in His footsteps and are also chanting the Hare Kṛṣṇa mahā-mantra, the effect is almost as potent as during the time of Lord Caitanya Mahāprabhu. Our preachers mainly belong to European and American countries, yet by the grace of Lord Caitanya they have tremendous success wherever they go to open branches. Indeed, everywhere people are very seriously chanting Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare.

Madhya 15.108-“One does not have to undergo initiation or execute the activities required before initiation. One simply has to vibrate the holy name with his lips. Thus even a man in the lowest class [caṇḍāla] can be delivered.PURPORTŚrīla Jīva Gosvāmī explains dīkṣā in his Bhakti-sandarbha (283):”Dīkṣā is the process by which one can awaken his transcendental knowledge and vanquish all reactions caused by sinful activity. A person expert in the study of the revealed scriptures knows this process as dīkṣā.” The regulative principles of dīkṣā are explained in the Hari-bhakti-vilāsa (2.3,4) and in Bhakti-sandarbha (283). As stated: “Even though born in a brāhmaṇa family, one cannot engage in Vedic rituals without being initiated and having a sacred thread. Although born in a brāhmaṇa family, one becomes a brāhmaṇa after initiation and the sacred thread ceremony. Unless one is initiated as a brāhmaṇa, he cannot worship the holy name properly.”According to the Vaiṣṇava regulative principles, one must be initiated as a brāhmaṇa. The Hari-bhakti-vilāsa (2.6) quotes the following injunction from the Viṣṇu-yāmala:“Unless one is initiated by a bona fide spiritual master, all his devotional activities are useless. A person who is not properly initiated can descend again into the animal species.”Hari-bhakti-vilāsa (2.10) further quotes:”It is the duty of every human being to surrender to a bona fide spiritual master. Giving him everything-body, mind and intelligence-one must take a Vaiṣṇava initiation from him.”The Bhakti-sandarbha (298) gives the following quotation from the Tattva-sāgara:”By chemical manipulation, bell metal is turned into gold when touched by mercury; similarly, when a person is properly initiated, he can acquire the qualities of a brāhmaṇa.”The Hari-bhakti-vilāsa (17.11,12) in discussing the puraścaryā process, quotes the following verses from Agastya-saṁhitā:”In the morning, afternoon and evening, one should worship the Deity, chant the Hare Kṛṣṇa mantra, offer oblations, perform a fire sacrifice, and feed the brāhmaṇas. These five activities constitute puraścaryā. To attain full success when taking initiation from the spiritual master, one should first perform these puraścaryā processes.”The word puraḥ means “before” and caryā means “activities.” Due to the necessity of these activities, we do not immediately initiate disciples in the International Society for Krishna Consciousness. For six months, a candidate for initiation must first attend ārati and classes in the śāstras, practice the regulative principles and associate with other devotees. When one is actually advanced in the puraścaryā-vidhi, he is recommended by the local temple president for initiation. It is not that anyone can be suddenly initiated without meeting the requirements. When one is further advanced by chanting the Hare Kṛṣṇa mantra sixteen rounds daily, following the regulative principles and attending classes, he receives the sacred thread (brahminical recognition) after the second six months.In the Hari-bhakti-vilāsa (17.4,5,7) it is stated:”Without performing the puraścaryā activities, one cannot become perfect even by chanting this mantra for hundreds of years. However, one who has undergone the puraścaryā-vidhi process can attain success very easily. If one wishes to perfect his initiation, he must first undergo the puraścaryā activities. The puraścaryā process is the life-force by which one is successful in chanting the mantra. Without the life-force, one cannot do anything; similarly, without the life force of puraścaryā-vidhi, no mantra can be perfected.”In his Bhakti-sandarbha (283), Śrīla Jīva Gosvāmī states:Of similar importance is dīkṣā, which is explained as follows in Bhakti-sandarbha (284):In other words, the chanting of the Hare Kṛṣṇa mahā-mantra is so powerful that it does not depend on official initiation, but if one is initiated and engages in pañcarātra-vidhi (Deity worship), his Kṛṣṇa consciousness will awaken very soon, and his identification with the material world will be vanquished. The more one is freed from material identification, the more one can realize that the spirit soul is qualitatively as good as the Supreme Soul. At such a time, when one is situated on the absolute platform, he can understand that the holy name of the Lord and the Lord Himself are identical. At that stage of realization, the holy name of the Lord, the Hare Kṛṣṇa mantra, cannot be identified with any material sound. If one accepts the Hare Kṛṣṇa mahā-mantra as a material vibration, he falls down. One should worship and chant the holy name of the Lord by accepting it as the Lord Himself. One should therefore be initiated properly according to revealed scriptures under the direction of a bona fide spiritual master. Although chanting the holy name is good for both the conditioned and liberated soul, it is especially beneficial to the conditioned soul because by chanting it one is liberated. When a person who chants the holy name is liberated, he attains the ultimate perfection by returning home, back to Godhead. In the words of Śrī Caitanya-caritāmṛta (Ādi 7.73):“Simply by chanting the holy name of Kṛṣṇa one can obtain freedom from material existence. Indeed, simply by chanting the Hare Kṛṣṇa mantra one will be able to see the lotus feet of the Lord.”The offenseless chanting of the holy name does not depend on the initiation process. Although initiation may depend on puraścaryā or puraścaraṇa, the actual chanting of the holy name does not depend on puraścaryā-vidhi, or the regulative principles.If one chants the holy name once without committing an offense, he attains all success. During the chanting of the holy name, the tongue must work. Simply by chanting the holy name, one is immediately delivered. The tongue is sevonmukha-jihvā-it is controlled by service. One whose tongue is engaged in tasting material things and also talking about them cannot use the tongue for absolute realization.ataḥ śrī-kṛṣṇa-nāmādi na bhaved grāhyam indriyaiḥsevonmukhe hi jihvādausvayam eva sphuraty adaḥ According to Caitanya-caritāmṛta (Madhya 17.134):”With these material senses, one cannot understand the transcendental holy name of the Lord or His form, activities and pastimes. However, when one actually engages in devotional service, utilizing the tongue, the Lord is revealed.”

NOI-4….
Not only is the chanter of the mahā-mantra purified, but the heart of anyone who happens to hear the transcendental vibration of Hare Kṛṣṇa, Hare Kṛṣṇa, Kṛṣṇa Kṛṣṇa, Hare Hare/ Hare Rāma, Hare Rāma, Rāma Rāma, Hare Hare is also cleansed. Even the souls embodied in lower animals, insects, trees and other species of life also become purified and prepared to become fully Kṛṣṇa conscious simply by hearing the transcendental vibration. This was explained by Ṭhākura Haridāsa when Caitanya Mahāprabhu inquired from him how living entities lower than human beings can be delivered from material bondage. Haridāsa Ṭhākura said that the chanting of the holy names is so powerful that even if one chants in the remotest parts of the jungle, the trees and animals will advance in Kṛṣṇa consciousness simply by hearing the vibration. This was actually proved by Śrī Caitanya Mahāprabhu Himself when He passed through the forest of Jhārikhaṇḍa. At that time the tigers, snakes, deer and all other animals abandoned their natural animosity and began chanting and dancing in saṅkīrtana. Of course, we cannot imitate the activities of Śrī Caitanya Mahāprabhu, but we should follow in His footsteps. We are not powerful enough to enchant the lower animals such as tigers, snakes, cats and dogs or entice them to dance, but by chanting the holy names of the Lord we can actually convert many people throughout the world to Kṛṣṇa consciousness. Contributing or distributing the holy name of the Lord is a sublime example of contributing or giving charity (the dadāti principle). By the same token, one must also follow the pratigṛhṇāti principle and be willing and ready to receive the transcendental gift. One should inquire about the Kṛṣṇa consciousness movement and open his mind in order to understand the situation of this material world. Thus the guhyam ākhyāti pṛcchati principles can be served.

Oct 26 1975 Mauritius, morning walk conversation

Prabhupada:Everyone thinks that he is right and everyone is wrong. We do not think like that. We take the words of the authority, that’s all. Or we have no respect(?). This is our program. That is the way of paramparā. Not only we accept, but our previous ācāryas, all the big, big ācāryas, they have accepted. Śukadeva Gosvāmī said. He is ācārya. Vyāsadeva says from the very beginning. Kṛṣṇa says. That’s all right. We take these authorities. We do not dream. That is not our process. Dream, your dream or my dream, this is all rascal. Dream is dream. Why do you think that your dream is right and my dream is wrong?

Brahmānanda: That’s why they’re always bickering with one another.

Prabhupāda: Yes. There is no standard idea. I dream some way; you dream some way. That’s all. What is this?

Cyavana: Seaweed.

Brahmānanda: It looks like a sponge.

Cyavana: Plant.

Prabhupāda: That is their defect. If my dream is wrong, why your dream should be right? That they did not conceive of, that “My dream is right(?).” And if you say that “Your dream is also wrong,” yes, I do not dream. I take the facts from the authority. We do not dream. Dream is dream, either yours or mine. It doesn’t matter.