RAW - no, and definitely not at +16
First, quibbling about the attack bonus if Sound Strike were a natural attack. The full wording of the natural attacks section of the Polymorph subschool rules states (emphasis mine):
In addition to these benefits, you gain any of the natural attacks of the base creature, including proficiency on those attacks. These attacks are based on your base attack bonus, modified by your Strength or Dexterity as appropriate, and use your Strength modifier for determining damage bonuses.
For a ranged attack, the attack bonus is BAB + DEX modifier of the subject of the spell (which is Personal). The Muse gets +16 because she has BAB of +8 and a DEX of 27 (giving a modifier of +8). A character who has cast Fey Form does not benefit from those modifiers, they have to use their own.
However, the more important question is whether this is a natural attack or not. The Muse appears in Bestiary 5. "Natural Attacks" have a lengthy entry in the Appendix 3: Glossary on p295 of the same book - the entire section is too long to reproduce here, but some relevant excerpts are:
Most creatures possess one or more natural attacks (attacks made without a weapon). These attacks fall into one of two categories: primary and secondary attacks. Primary attacks are made using the creature's full base attack bonus and add the creature's full Strength bonus on damage rolls. Secondary attacks are made using the creature's base attack bonus -5 and add only 1/2 the creature's Strength bonus on damage rolls.
The Damage Type column refers to the sort of damage that the natural attack typically deals: bludgeoning (B), piercing (P), or slashing (S)…
Some fey, humanoids, monstrous humanoids and outsiders don't have natural attacks. These creatures can make unarmed strikes, but treat them as weapons for the purpose of determining attack bonuses, and they must use the two-weapon fighting rules when making attacks with both hands...
The takeaways from this are:
- natural attacks are using strength to deal bludgeoning, piercing or slashing damage.
- some fey do not have natural attacks, but can attack unarmed (as per the melee attack listed for the Muse). Note that the mention of fey specifically is in Bestiary 5 (the book the Muse is from) but is not in the linked PSFRD entry.
Based on this, the sonic strike is not a natural attack.
Some of the comments and answers are noting that sonic strike is not listed as a special attack or special ability, hence it must be a natural attack. While I understand that arguing about writer intent turns into an opinion-based exercise in futility, it needs to be pointed out that in this instance we already know that the entry for sonic strike is incomplete. There is no range listed! RAW, sonic strike is a direct fire attack with infinite range that can be used at line of sight with no range penalties! (The same issue exists with the Flytrap Leshy on p156 of the same book, its acidic spittle can go on ad infinitum too - pretty good for a CR4 monster. Maybe that's why it doesn't seem to have made its way into the PSFRD.) For comparison, the Piercing Hymn of the Choral Angel also does 4d6 sonic damage but is a defined power with a range of 90'.
TL;DR - sonic strike is not a natural attack and the GM needs to work out its range and any other details in their campaign.
RAW, you should get all 5 Sonic attacks
The Muse doesn't get iterative attacks with Sonic Strike
As noted by The Dark Wanderer in their comment, the Muse doesn't get iterative attacks with sound strikes. Instead, the creature only gets an arbitrary number of attacks (5), all at the same bonus (+16).
But she would do so if those attacks were normal weapon attacks
The rules on natural attacks say:
You do not receive additional natural attacks for a high base attack bonus.
However, usually, per the attack bonus rules, you have bonus attacks for BAB higher than +5. The Muse has 17 HD, and Fey have BAB equal to 1/2 their HD, so the BAB is 17/2=+8, giving the Muse at least one Iterative attack at -5.
The only exception from this rule are natural weapons, with the appropriate the rule quoted above.
The Polymorph subschool says that you get all the natural attacks
Because all the 5 attacks are instead made at the same bonus (+16), those attacks are clearly natural weapons, and you should get them when you turn into a Muse, per the Polymorph subschool rules.
In addition to these benefits, you gain any of the natural attacks of the base creature, including proficiency in those attacks.
The attack bonus will most likely not be +16
As a level 5 Druid casting Fey Form I, your BAB is +3. You add your Dexterity modifier here, and you also add any feats applicable to ranged attacks, e.g. Precise Shot. So, if you have Dex 16 and no special feats, you roll with a +6 bonus to hit, which is not that bad against touch AC, averaging around 12 for CR 5 and onwards.
Arguably, it could go either way.
Sound Strikes isn't a listed Natural Attack; granted it specifies that the list is only "some of the most common types of natural attacks". However, it is listed as a ranged attack that isn't a weapon so it can be considered a Natural Attack per the transmutation [polymorph] rules.
However, there also existed a hard distinction in D&D 3.5 that is a Special Attack. (Special Abilities that are not Special Qualities). It seems, based on the context of the question that prompted the answer, that Pathfinder seems to have soft-adopted this definition without actually having it written down. Regardless, the potential remains to pull this important portion to note from that answer
Special Attacks are listed under Offence section of creature's entry, so you may more or less easily sort them out.
If a GM were to consider Sound Strikes a Special Ability (Attack), then Fey Form would not grant it unless it is specifically called out in the spell (it is not).
Unfortunately, this distinction is not well represented in Pathfinder creature statblocks. For example, the Thorny has a similar (if much weaker) natural ability to perform ranged attacks that aren't capital-N.A. Natural Attacks. However it was written differently; the details of the attack are in it's Special Abilities block (likely due to the variable number of and poisonous nature of its attack). The Terrasque is in a similar position for different reasons. Examples of situations similar to the Muse are harder to find because such an ability is not explained beyond its name, attack roll, and damage.
As a proposal for balance... a GM could consider allowing the ranged attack, but only allowing it once per turn. This would put it in line with other natural attack while still allowing it to be a powerful choice in many situations.
Also notable... it is Sonic damage. Anything with the spellcasting capability and a brain could become basically immune to the attack with Resist or Protection from [Sonic] Energy.