Reconstruction of audio signal from Spectrogram
If the spectrogram was computed as the magnitude of short time fourrier transforms from overlapping windows, then the spectrogram contains implicitly some phase information. 

The following iterations do the job :

$$x_{n+1} = \text{istft}(S\cdot\exp(i\cdot\text{angle}(\text{stft}(x_n))))$$

$S$ is the spectrogram, $\text{stft}$ is the forward-short time Fourier transform, $\text{isft}$ is the inverse-short time Fourier transform.