[c#] An object reference is required to access a non-static member

You should make your audioSounds and minTime members static:

public static List<AudioSource> audioSounds = new List<AudioSource>();
public static double minTime = 0.5;

But I would consider using singleton objects instead of static members instead:

public class SoundManager : MonoBehaviour
{

    public List<AudioSource> audioSounds = new List<AudioSource>();
    public double minTime = 0.5;

    public static SoundManager Instance { get; private set; }

    void Awake()
    {
        Instance = this;
    }

    public void playSound(AudioClip sourceSound, Vector3 objectPosition, int volume, float audioPitch, int dopplerLevel)
    {    
        bool playsound = false;
        foreach (AudioSource sound in audioSounds) // Loop through List with foreach
        {  
            if (sourceSound.name != sound.name && sound.time <= minTime)
            {
                playsound = true;
            }
        }

        if(playsound) {
            AudioSource.PlayClipAtPoint(sourceSound, objectPosition);
        }

    }
}

Update from September 2020:

Six years later, it is still one of my most upvoted answers on StackOverflow, so I feel obligated to add: singleton is a pattern that creates a lot of problems down the road, and personally, I consider it to be an anti-pattern. It can be accessed from anywhere, and using singletons for different game systems creates a spaghetti of invisible dependencies between different parts of your project.

If you're just learning to program, using singletons is OK for now. But please, consider reading about Dependency Injection, Inversion of Control and other architectural patterns. At least file it under "stuff I will learn later". This may sound as an overkill when you first learn about them, but a proper architecture can become a life-saver on middle and big projects.

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