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A Plated Shofar: 
It is forbidden to have any intervention between the mouth of the blower and the Shofar material. Therefore if one plated a Shofar with gold in the area where the mouth rests, in order to beautify it, the Shofar is invalid. This applies even if the gold only covered the external part of the Shofar along its length, nevertheless if the gold covers the narrow end the Shofar is invalid. [This applies even if the area of the mouth is covered with external Shofar material.]
The area covered by the mouth is not plated: If the plating is distanced from the narrow end of the Shofar and hence the lips of the blower do not rest on the gold plating, then the Shofar is valid so long as the plating did not alter the sound of the Shofar. However if one knows that the sound has been altered due to the plating then the Shofar is invalid even if there was only a slight change in sound.
If one is unsure if the sound altered: If one is unsure whether the sound of the Shofar has altered due to the coating the Shofar remains valid as most probably the sound of the Shofar did not change simply due to a mere coating.
If the plating extends past the length of the Shofar: All the above refers to a coating which was placed over the thickness or width of the Shofar and does not extend past the end of the Shofar. If however the coating extends past the end of the Shofar then the Shofar is invalid as will be explained in the next Halacha.
The Shofar is invalid if the plating covers the area of the Shofar that the lips of the blower rests, or if one notices that the coating has changed the sound of the Shofar. If the sound has not changed and the coating is not within the area that the lips rest, it remains valid.
If the inside of the Shofar is plated is it valid?
If the inner part of the Shofar is covered with gold or the like the Shofar is invalid even if the sound did not change.
May one even initially coat a Shofar in a valid way?
Seemingly one should not coat a Shofar with any material, even if the Shofar will remain valid, as at times the sound of the Shofar changes due to the coating and one will not be aware of this change. This certainly applies to gold material of which some Poskim write is improper to be placed on a Shofar due to its use in the sin of the golden calf.
 586/16; Michaber 586/17
 This applies to any coating. The Mahril writes the reason why specifically gold is mentioned is because gold was used to make the golden calf and therefore this material cannot be used as a defense for the Jewish people. [Kaf Hachaim 586/116]
 The reason: The reason for this is because the lips of the blower rests on the gold and there is thus an interval between the lips of the blower and the Shofar material. [Admur ibid; See Avnei Nezer 432-433; Dovev Meisharim 1/66 as for why the law here is different than by Lulav 651 in which case an item of beauty is not a Chatzitza]
 The reason: As nevertheless the lips of the blower rest partially on the gold and there is hence an interval between his lips and the Shofar. [ibid]
The Michaber 586/16 quotes the Braisa which states that if the gold was placed in the area of the mouth it is invalid while if it was placed not in that in that area it is valid. The Michaber then brings two different ways of defining “area of the mouth” as found in Rishonim. The mouth of the Shofar contains an outer slope and inner slope, similar to a kernel of barley which has two slanted sides. [M”B 586/19; Kaf Hachaim 586/120] Some [Ran] explain that the “area of the mouth” means that if the gold coated the inner slant of the mouth of the Shofar then it is invalid while if it coated the external slant of the mouth of the Shofar, then it is valid, even though the lips rest on it. Others [Rosh] explain that whether the gold covered the inner or outer slope of the narrow end it is invalid. The Levush rules that even if the coating covered past the slope of the external side nevertheless if the lips of the blower cover that coating it is invalid. Admur here rules like this opinion of the Levush and this is the meaning of his wording “the length of the Shofar”.
 Avnei Nezer 432-433
 The reason: The reason why an alteration of sound invalidates the Shofar is because this reveals that the sound which is heard is the sound of the Shofar and of the plating and a Shofar is only valid if it alone is responsible for its sound and not any additional substances. [ibid]
 It is unclear what the definitions of these terms “Oviy” “Rachav” and Orech” are. In English Oviy refers to thickness, Rachav to width and Orech to length. Poskim use these words to refer to different parts of the Shofar although some use it to describe one area while others use it to describe a different area. [See Michaber 586/16; Aruch Hashulchan 586/30] For this reason it is very difficult to determine what exactly here Admur refers to in his wording of thickness and width. One cannot say that thickness means the inside of the Shofar as the Michaber clearly rules that any coating on the inside is invalid. [see Q&A!] Now although Admur does not record this ruling there are no Poskim which dispute it and hence it is hard to believe that he argues on it. Furthermore he would have rather used the word “Befnim” which is the wording the Michaber himself uses to refer to it, if he intended to say the inner part. Possibly the term thickness here refers to the outer slope of the wide end of side of the Shofar. [See Michaber 586/16 for one opinion who defines thickness in this way] while the width refers to the external part of the Shofar. Hence Admur is saying that whether one coated the outer slope of the thickness of the wide end or the outer part of the Shofar it is valid so long as it does not extend past the length of the Shofar and the sound has not changed it is valid. If however the coating covers the inner slope of the wide end or any slope of the narrow end it is invalid. Vetzaruch Iyun.
 Michaber 586/16 based on Braisa; M”B 586/70; Vetzrauch Iyun Gadol why Admur completely omitted this law from 586/16 and 17 and merely stipulates that it cannot extend past the length of the Shofar. See also Aruch Hashulchan 586/30.
 As it is as if one is blowing with gold and not with the Shofar. [M”B ibid Based on Levush 586/16]
 Based on Admur 586/18
 Kaf Hachaim 586/116