densya no naka de ha tuution ga denai you ni, sumaho wo muon ni site iru.

電車で often means by train as a means of transportation.

• 学校へ電車で行く = I go to school by train

But 電車の中で specifically means inside the train.
In this sentence, the speaker is talking about what they do while they are physically on the train, so 電車の中で is clearer.

では is simply で + は.

• で marks the setting/situation
• は makes that setting the topic, often with a slight contrast

So 電車の中では means something like:

• when I’m on the train
• as for on the train
• at least on the train

The は can suggest contrast, such as:
I may not always do this, but on the train I do.

A common rule of thumb is:

• に = location of existence, destination, specific point
• で = location/setting where an action happens

Here, the sentence is about the action/state of keeping the phone silent in that setting, so で is natural.

Compare:

• 電車の中にいる = to be in the train
• 電車の中でスマホを無音にしている = to keep the phone silent in the train

This is about intransitive vs. transitive wording.

• 出る = to come out, be emitted, be produced
• 出す = to put out, produce

So:

• 通知音が出ない = the notification sound does not come out
• 通知音を出さない = not produce the notification sound

Both can work, but they focus a little differently:

• 通知音が出ないように focuses on the result
• 通知音を出さないように focuses more on the person’s action

Because 出ない is intransitive, 通知音 takes が.

Because in Japanese, sounds often come out.

Very common expressions are:

• 音が出る = sound comes out / sound is produced
• 声が出る = voice comes out
• 涙が出る = tears come out

So 通知音が出る is a very natural Japanese way to say that a notification sound is emitted.

Here, ～ないように means so that ... not or in order to prevent ....

So:

• 通知音が出ないように = so that notification sounds won’t come out

This pattern is very common when talking about trying to achieve or avoid a certain result.

Examples:

• 忘れないようにメモする = I make a note so that I won’t forget
• 風邪をひかないように気をつける = I’m careful so that I won’t catch a cold

Usually ように is the more natural choice here.

A rough difference is:

• ために often expresses a more direct, intentional purpose
• ように often expresses aiming for a result, especially with things that are not fully under direct control or are phrased as a state/result

Since 通知音が出ない is a result/state, ように fits very well.

So 通知音が出ないために is not impossible in every context, but 通知音が出ないように sounds more natural here.

無音 means no sound / silent.

The pattern A にする means to make something A or to set something to A.

So:

• スマホを無音にする = to set the smartphone to silent

The particle に marks the state the phone is being changed into.

Similar patterns:

• 部屋をきれいにする = make the room clean
• 音を小さくする = make the sound quieter

～ている here shows a continuing state.

After you set your phone to silent, it stays in that state. So:

• 無音にする = set it to silent
• 無音にしている = keep it on silent / have it on silent

So this sentence does not mean I am in the middle of silencing it right now.
It means I keep my phone silent in that situation.

It can also suggest a habit:

• When I’m on the train, I keep my phone on silent.

It is omitted.

Japanese very often leaves out the subject when it is obvious from context. In this sentence, the understood subject is usually:

• I
• or whatever person the conversation is already about

So even though 私 does not appear, the sentence naturally means something like I keep my phone on silent...

Yes, you could say something else.

• スマホ is a very common casual word for smartphone
• スマートフォン is the full form

For the silent setting, many people would also say:

• マナーモードにしている
• サイレントモードにしている

These may sound more like the actual phone setting name.
無音にしている is understandable and natural enough, but it sounds a bit more literally like making it silent / muting it.