Since the introduction of the tab audio playback indicator¹, there are been a large number of requests of people asking for the ability to mute a tab with this indicator and here's the official answer which makes sense:

After much debate, we decided not to proceed with a tab mute control, as this crosses a very important line: If we provide Chrome controls for content, we're implying that Chrome should take on a responsibility to police content.

Today, users are (rightfully) mad at misbehaving content for doing things like auto-playing annoying ad audio, but they should continue to pressure web site authors to change this behavior.  Also, some have pointed out that there is already a mute button to the right of the audio indicator (the "X").  In all seriousness, note that many web pages will register onClose() events to monitor when users leave their site.  Thus, closing the tab will be a very strong signal to the web sites that their annoying ads are scaring all their users away!

For "behaving" content, we think it's reasonable for a user to click on a tab and use the content's media controls to stop playback.  In this case, a Chrome tab mute control would be redundant.  This redundancy is bad since it can confuse users (e.g., to play a video and forget that a tab was muted days ago); and, based on experience, confused users often report unexpected behaviors as browser bugs, which would be a big distraction to the Support and Eng staff.

The best part for me is that is that even though this feature won't be built in Chrome for the reasons mentioned below, a proposal for a chrome.tabaudio API has been filed² which would give sound control to Chrome Extensions when reviewed and approved by the chromium team.

¹ http://chrome.blogspot.fr/2014/01/everyone-can-now-track-down-noisy-tabs.html
² https://docs.google.com/document/d/1kR1sUg6QOMJDE2c6jZgm15g1L89GuVx7HAGfcIqqbrY/edit

Source: https://code.google.com/p/chromium/issues/detail?id=3541
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