Does the speed of sound depend on the speed of the medium?

[anonymous99]

Homework Statement

Methane is transported along a 4km pipeline at a Mach number of 0.3 and
temperature 30◦C. A valve positioned 2km from the inlet begins to close, creating a pressure wave up and down the pipe. Calculate the time it takes for the
pressure wave to reach a) the inlet, and b) the outlet of the pipe. [for methane:
Cp = 2.2537kJ/kgK, Cv = 1.7354kJ/kgK, R = 0.5182kJ/kgK

Relevant Equations

The answers given are 6.3s for inlet and 3.4s for outlet, which I was able to obtain by dividing 2000/c-u and 2000/c+u.

This means the sound wave reaches the outlet faster as it travels in the same direction as the medium. But I was reading online that speed of sound is independent of the medium so I don't know why my professor used this approach. If speed of sound was dependent on the medium, then wouldn't shock waves be impossible because the sound wave would always travel at c+speed of medium?

 

[PeroK]

But I was reading online that speed of sound is independent of the medium so I don't know why my professor used this approach. If speed of sound was dependent on the medium, then wouldn't shock waves be impossible because the sound wave would always travel at c+speed of medium?

Can you explain what you are saying here?

The sound wave in a medium moves relative to the medium, but generally has constant speed for a given medium (at a given temperature and pressure etc.). If the medium is moving relative to something else, then you have to take that into account.

In this case, the medium is moving relative to a pipe.

 

[anonymous99]

I worked out c to be 299.3m/s. Does that mean that is the speed of the sound wave relative to the methane gas so for a stationary observer, he would see the sound wave moving at 299.3+speed of methane?

 

[PeroK]

I worked out c to be 299.3m/s. Does that mean that is the speed of the sound wave relative to the methane gas so for a stationary observer, he would see the sound wave moving at 299.3+speed of methane?

It would have to be. Think of people talking in an aircraft and the speed of those sound waves to a ground observer.

The sound travels normally inside the aircraft. From a ground reference frame, everything inside the aircraft is moving at whatever + the aircraft's ground velocity.

 

[anonymous99]

Ok, thanks for clearing that up for me.