To classify images we are using the tensorflow incection v3 NN.
Is there a similar approach to classify sounds? As for example to be able to recognize the person who is talking or classify a general sound?
There are probably many different approaches to doing what you are talking about, but the most common would probably be using long short term memory recurrent neural networks to operate on the data through time. You would be able to train your neural network to do the things that you want to do such as classify the speaker, and classify noises into different categories. However, to train neural networks like these, it requires a lot of training data as does any other deep neural network. So, if you want to apply these kinds of neural networks to practical problems you will need a lot of training data. Or, you could just use a smaller simpler neural network.
I will add on top of another answer which proposed to use LSTM network.
LSTMs and RNNs in general are great tools in speech recognition that can model sequential information inherently. There were several ground-breaking papers which used RNNs, e.g. Deep Speech: Scaling up end-to-end speech recognition and its second version.
Recently we have found that Convolutional Neural Networks (CNNs) are also great with speech/sound even though they do not model sequential information inherently. There was a problem that it wouldn't be able to model long-term dependencies due to small receptive field of kernels (even though they are stacked in many layers). WaveNet: A Generative Model for Raw Audio was one of the first papers that successfully used CNN to generate speech. One of their main contributions was usage of dilated convolutions which allowed them to model long-term dependencies. In principle, you can use a similar architecture but instead of predicting another point in time as done in Wavenet you can do your own classification in the last layer (while also changing the loss to cross-entropy for example). You might also want to look at the papers that cite Wavenet because deep learning is quickly growing field.
Additionally there is an amazing lecture on Speech Recognition which you might find very valuable and it's relatively recent too.