Entropy is a feature of a random variable. A given file has zero entropy, since it is constant. Entropy makes sense in many situation in which there is no channel, and you can apply it to a random ensemble of, say, WAV files, generated from a given source. In this case, your $x$ is the entire WAV file.
The actual WAV file (excluding the header) can be thought of being generated by some Markovian source. This source produces sounds amplitudes ("samples") in a sequence, each one depending on the ones preceding it. After running the process for very long, the entropy of each sample (more accurately, the conditional entropy given the preceding samples) gets very close to some limiting value, which we define to be the entropy of the source. The entropy of $N$ samples is $N$ times that number (in the limit; again, more accurately, we are measuring the conditional entropy). Lempel and Ziv showed that if the sample entropy is $H$ bits, then their algorithm compresses $N$ samples to $HN + o(N)$ bits, with high probability (the probability is over the samples). Lempel–Ziv compression is quite popular in practice, used for example in the popular
Due to this result of Lempel and Ziv, the entropy of a source can be approximated by compressing a long sequence of samples using the Lempel–Ziv algorithm. This doesn't estimate the entropy of the specific samples, which is not a well-defined concept (a constant sequence has zero entropy), but rather the entropy of the source generating it.
A related concept is algorithmic entropy, also known as Kolmogorov complexity. It is the length of the shortest program generating your file. This quantity does make sense for an individual file. In the case of a file generated by a random source, the Lempel–Ziv theorem shows that the algorithmic entropy of a file is bounded, with high probability, by its Shannon entropy. Unfortunately, algorithmic entropy isn't computable, so it's more of a theoretical concept.
To complete the picture, I suggest reading Shannon's paper on Prediction and entropy of printed English for a different approach to estimating the entropy of a source.