Do quieter sounds travel at the same speed but for less distance?
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The one word answer is no. The once sentence answer is that “speed of sound” is not a question you can ask without adding a lot more stuff. Unlike with light, there is no concept of speed of sound absent context.
The speed of sound depends on the temperature, density and type of material the wave is propagating in. Temperature is more than a simple variable. The equations for determining the speed of sound in solids, gases and liquids are completely different.
It’s not even as simple as asking questions like “what is the speed of sound in liquid water?” Calculations for the speed of sound in the ocean depend on temperature, depth and even salinity.
Additionally, similar to how a glass prism can break up light, material can alter the sound of some frequencies differently than others. Speed of sound will also vary by frequency with higher frequencies traveling faster.
Different frequencies can even behave differently in the same medium. Imagine the sound of loud music in the room next door. In this case, higher frequencies are being reflected by the wall while while lower frequencies will pass through the wall so you only hear the deep rumbles.
If that’s not complicated enough, the speed of sound also depends on the type of wave. Pressure and transverse waves behave differently.
This is such a complex topic that the formulas used will always ignore factors that are not likely to be important for the calculation. For example, you can find formulas that will determine the speed of sound in air depending on temperature. But that’s incomplete. Other factors, such as humidity and altitude will also affect the speed of sound in air.
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