Флейта звучала тише, чем саксофон, поэтому учитель попросил играть смелее.

Because флейта is a feminine singular noun, and the past tense in Russian agrees with the subject in gender and number.

• флейта = feminine singular
• past tense of звучать becomes звучала

Compare:

• саксофон звучал = the saxophone sounded
• флейта звучала = the flute sounded

So звучала tells you that the thing doing the sounding is feminine.

Тише is the comparative form meaning more quietly or quieter.

It comes from тихо = quietly / soft and is related to тихий = quiet, soft.

In this sentence, it works adverbially: it describes how the flute sounded.

• Флейта звучала тише = The flute sounded quieter / more softly

Russian often uses the same comparative form in places where English might use either an adjective or an adverb, depending on the translation.

Чем means than in comparisons.

So:

• тише, чем саксофон = quieter than the saxophone

This is the normal, straightforward way to make a comparison in Russian:

• comparative form + чем
  • what you compare it to

Examples:

• быстрее, чем я = faster than me / than I am
• интереснее, чем фильм = more interesting than the film

After чем in this kind of comparison, Russian normally uses the nominative form.

So:

• чем саксофон = than the saxophone

Here саксофон is in its basic dictionary form, nominative singular.

Learners sometimes expect another case, but with чем this nominative pattern is very common and standard.

Поэтому means therefore, so, or that’s why.

It links the first idea to the result:

• Флейта звучала тише, чем саксофон = The flute sounded quieter than the saxophone
• поэтому учитель попросил играть смелее = so the teacher asked for bolder playing / asked them to play more boldly

So поэтому shows cause and result.

Попросил is the perfective past form of просить. It usually suggests a single completed act of asking.

Here that fits well: the teacher made one request in response to what he heard.

• попросил = asked, made the request
• просил = was asking / asked repeatedly / used to ask, depending on context

So попросил sounds more natural if the teacher reacted once and said something like Play more boldly.

After verbs like попросить in Russian, it is very common to use an infinitive to say what someone asked another person to do.

So:

• попросил играть смелее = asked someone to play more boldly

This is similar to English:

• asked to play more boldly

Russian can omit the person being asked if it is obvious from context. For example, the teacher probably asked the flutist or the students, but that does not need to be stated explicitly.

Играть is imperfective, and it focuses on the activity or manner of playing, not on completing a piece.

Here the teacher is commenting on how they should play:

• more boldly
• with more confidence
• with stronger presence

That makes играть the natural choice.

If you used сыграть, it would sound more like to perform/play something through to completion, which is not the main idea here.

Literally, yes: смелее is the comparative of смело / смелый, so it means more boldly, more confidently, or literally braver.

In a musical context, though, it usually means something like:

• play with more confidence
• play more assertively
• don’t be timid

So it is not really about courage in a dramatic sense; it is more about performance style and presence.

Not exactly.

• звучать = to sound
• играть = to play

In this sentence, that distinction matters:

• Флейта звучала тише = The flute sounded quieter
  • this describes the result, what was heard
• учитель попросил играть смелее = The teacher asked them to play more boldly
  • this describes the action the teacher wanted

So first the sentence describes the sound, then it gives the teacher’s instruction.

Russian often leaves out words that are clear from context.

So учитель попросил играть смелее literally looks like:

• the teacher asked to play more boldly

But the meaning is:

• the teacher asked someone to play more boldly

That someone is understood from the situation, probably:

• the flutist
• the student
• the players

English often prefers to state the object more clearly, but Russian can omit it when it is obvious.

Yes, that is a good natural translation.

A few natural English versions are possible:

• The flute sounded quieter than the saxophone, so the teacher asked them to play more boldly.
• The flute was softer than the saxophone, so the teacher asked for more confident playing.
• The flute sounded quieter than the saxophone, so the teacher asked the player to be bolder.

The exact English wording depends on style, but the Russian grammar points stay the same.