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I've got this wonderful conundrum with a WAV file, whereas I cannot detect it's actual sample size (i.e. how many bits are in a sample) and the number of channels.

geek@liv-inspiron:~$ soxi file.wav

Input File : 'file.wav'
Channels : 2
Sample Rate : 44100
Precision : 16-bit
Duration : 00:03:19.56 = 8800596 samples = 14967 CDDA sectors
File Size : 35.2M
Bit Rate : 1.41M
Sample Encoding: 16-bit Signed Integer PCM

MPlayer2 reports the following (but I can only hear noise):

geek@liv-inspiron:~$ mplayer file.wav 
MPlayer2 2.0-701-gd4c5b7f-2ubuntu2 (C) 2000-2012 MPlayer Team

Playing file.wav.
Detected file format: WAV / WAVE (Waveform Audio) (libavformat)
[wav @ 0x7f21516c9600]max_analyze_duration reached
[lavf] stream 0: audio (pcm_s16le), -aid 0
Load subtitles in .
Selected audio codec: Uncompressed PCM [pcm]
AUDIO: 44100 Hz, 2 ch, s16le, 1411.2 kbit/100.00% (ratio: 176400->176400)
AO: [alsa] 44100Hz 2ch s16le (2 bytes per sample)
Video: no video
Starting playback...

While MPlayer outputs actual sound, and seems to detect a DTS format:

geek@liv-inspiron:~$ mplayer file.wav 
MPlayer 1.1-4.8 (C) 2000-2012 MPlayer Team

Playing file.wav.
libavformat version 54.20.3 (external)
Audio only file format detected.
Load subtitles in ./
==========================================================================
Opening audio decoder: [ffmpeg] FFmpeg/libavcodec audio decoders
libavcodec version 54.35.0 (external)
AUDIO: 44100 Hz, 2 ch, floatle, 1411.2 kbit/50.00% (ratio: 176400->352800)
Selected audio codec: [ffdca] afm: ffmpeg (FFmpeg DTS)
==========================================================================
AO: [pulse] 44100Hz 2ch floatle (4 bytes per sample)
Video: no video
Starting playback...

And if I play it with VLC which also outputs actual sound, it reports:

Type: Audio
Codec: DTS Audio (dts )
Channels: 3F2R/LFE
Sample rate: 44100 Hz
Bitrate: 1411 kb/s

Some quick math yields 1411 ∕ 44.1 ≈ 31.995465, which implies a 32-bit sample size. So which one is it: 16-bit or 32-bit? Or is it 16-bit per channel?

And how many channels does it have? 2 as in Stereo or 5 as in DTS? The info is again conflicting...

In other words, is there a tool that can accurately report the technical data for a WAV file, without getting confused by erroneous headers?

As pointed out in this question, an excellent utility for this task is MediaInfo.

MediaInfo is a convenient unified display of the most relevant technical and tag data for video and audio files.

geek@liv-inspiron:~$ mediainfo file.wav 
General
Complete name : file.wav
Format : Wave
File size : 33.6 MiB
Duration : 3mn 19s
Overall bit rate mode : Constant
Overall bit rate : 1 411 Kbps

Audio
Format : DTS
Format/Info : Digital Theater Systems
Mode : 14
Format settings, Endianness : Little
Codec ID : 1
Duration : 3mn 19s
Bit rate mode : Constant
Bit rate : 1 411.2 Kbps
Channel(s) : 6 channels
Channel positions : Front: L C R, Side: L R, LFE
Sampling rate : 44.1 KHz
Bit depth : 24 bits
Compression mode : Lossy
Stream size : 33.6 MiB (100%)

This would confirm that the specific file is DTS with 6 channels, but interestingly that the sample size is actually 24 bits and strangely that the compression mode is lossy.

One can also use this utility via a GUI: mediainfo-gui.

Looks like dts-wav. Many of these files have a header format ID which suggests PCM, but the actual byte stream is DTS.
This explains the soxi output.

If you have a recent version (2007 or later) of ffmpeg/libavcodec installed, mplayer should be able to detect that and use the appropriate non-PCM codec.

The VLC output implies you have DTS with a 5.1 configuration (6 channels).

For a useful online, drag-and-drop "Free Online EXIF Viewer" that will give you all the data you want an more, try

https://www.get-metadata.com/

If you want details of what you can get from that site, check out this answer on SuperUser.