11 year old girl aggressive towards sibling

She'll be responding with built-up resentment, it's not out of the blue. It's a bit like self defence and a survival mode, everyone has a limit. Imagine walking around all day and at whim someone starts popping gum in your ear. And it continues when you weren't looking or expecting it... for years.

Noise is a difficult one. Certain frequencies can be grating. Kant (philosopher) appropriated music as the worst of the aesthetics because it could penetrate / invade your senses when you weren't desiring it. Frequency and Noise are used for sonic weaponry and for prison torture. It is no small matter. You also need to make sure the sister making the noise isn't antagonising the other as it seems to keep happening. 

Let's call them Y = sister making the noise and X = for your undiagnosed daughter.

Do they have seemingly pleasant conversations occasionally? Perhaps the car is a good place for them to wear headphones and use digital media of some sort. Allow it to become a place where they can intentionally be in their own world, with their own music or game. If nothing else - for safety.

Silence is actually not a terrible thing. We can find other ways to communicate. In theatre classes or elocution classes, one is taught how to craft the voice in pleasant ways. We do this for business and diplomats. There IS an art to this and it wouldn't hurt in the least to explore all the possibilities with vocal expressions. In fact, it might give daughter Y further success in the world to see this challenge and seize the opportunity to create an aesthetic with her voice. Singing lessons can help, too. These are really enjoyable explorations and crafting the Self isn't just for a middle class art student who goes in to upper management. 

It's important to help both X and Y explore matters of aesthetics with sound. I work in the field and just left a good deal of information on sound regarding another young autist who's having extreme difficulty with it: https://community.autism.org.uk/f/parents-and-carers/26859/severe-sensory-to-sounds-and-headbanging/236181#236181

The most important complexity to note is autistic children can have extremely sensitive senses. Which can be amazing for a specialised field. Not just this, but it is the intensity at which they feel which is a element at play. We cannot dull our senses for various  reasons both scientifically and psychologically noted. Because of this, we are subjected to the elements and can often go our whole lives feeling incredibly unprotected and violated. 

If your daughters can learn to be respectful toward one another, this is a start. But if Y is doing this on purpose because she secretly enjoys how out of control her sister becomes, it is another level of problem to solve.

She'll be responding with built-up resentment, it's not out of the blue. It's a bit like self defence and a survival mode, everyone has a limit. Imagine walking around all day and at whim someone starts popping gum in your ear. And it continues when you weren't looking or expecting it... for years.

Noise is a difficult one. Certain frequencies can be grating. Kant (philosopher) appropriated music as the worst of the aesthetics because it could penetrate / invade your senses when you weren't desiring it. Frequency and Noise are used for sonic weaponry and for prison torture. It is no small matter. You also need to make sure the sister making the noise isn't antagonising the other as it seems to keep happening. 

Let's call them Y = sister making the noise and X = for your undiagnosed daughter.

Do they have seemingly pleasant conversations occasionally? Perhaps the car is a good place for them to wear headphones and use digital media of some sort. Allow it to become a place where they can intentionally be in their own world, with their own music or game. If nothing else - for safety.

Silence is actually not a terrible thing. We can find other ways to communicate. In theatre classes or elocution classes, one is taught how to craft the voice in pleasant ways. We do this for business and diplomats. There IS an art to this and it wouldn't hurt in the least to explore all the possibilities with vocal expressions. In fact, it might give daughter Y further success in the world to see this challenge and seize the opportunity to create an aesthetic with her voice. Singing lessons can help, too. These are really enjoyable explorations and crafting the Self isn't just for a middle class art student who goes in to upper management. 

It's important to help both X and Y explore matters of aesthetics with sound. I work in the field and just left a good deal of information on sound regarding another young autist who's having extreme difficulty with it: https://community.autism.org.uk/f/parents-and-carers/26859/severe-sensory-to-sounds-and-headbanging/236181#236181

The most important complexity to note is autistic children can have extremely sensitive senses. Which can be amazing for a specialised field. Not just this, but it is the intensity at which they feel which is a element at play. We cannot dull our senses for various  reasons both scientifically and psychologically noted. Because of this, we are subjected to the elements and can often go our whole lives feeling incredibly unprotected and violated. 

If your daughters can learn to be respectful toward one another, this is a start. But if Y is doing this on purpose because she secretly enjoys how out of control her sister becomes, it is another level of problem to solve.