Why does sound propagate in all directions from source? Recently I've read about sound wave propagation. Let's look on loudspeaker. If it creates sound waves by pushing and pulling the air in front of it , how we can hear sound when we are behind the loudspeaker or above and under?
How does sound travel in all directions from loudspeaker's membrane?

 A: Reflections from hardish surfaces and diffraction.  The housing and the object on which the loudspeaker stands will also vibrate and produce sound waves.
A: @Farcher's answer says it all in a nutshell. Basically, the dominant factor behind the sound reaching behind the loudspeaker, is reflection from surrounding objects, and the vibration of the loudspeaker itself (not very clear sound). Another important factor, is diffraction which is common to waves. The sound waves diffract around the corners of the soundbox, producing disturbances behind the box as well. One more thing: the picture you gave shows a sort of sound 'beam'. In general, the wave is much more spread out even at the box membrane.
A: It depends on the geometry and vibrational mode of the vibrating source generated.  It can be spherical, cylindrical or plane wave fronts.
Use turning fork as an example, we can regard it as a quadruple source (see the link here) and also animations for vibrational mode of tuning fork.
A: If the membrane diameter is small compared with the wavelength in air (which is usually the case with loudspeakers) then the sound will travel omnidirectionally.  Think of extending your curves showing the sound wave, into full circles.
With low frequencies diffraction is much easier - it is as though the box is not really there at all.
