For a visual picture of waves, you may want to browse through some of these simulations: they show animation of various concepts from waves and sound. 
Most of these are from Daniel Russell, who was a student at Bradley Univ.,
where I taught for a few years, and is now a professor at Penn State U. 

https://www.acs.psu.edu/drussell/demos.html  

What is a wave?

https://www.acs.psu.edu/drussell/Demos/waves-intro/waves-intro.html  

https://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html 


Wave motion in space and time 

https://www.acs.psu.edu/drussell/Demos/wave-x-t/wave-x-t.html  


Reflection of waves on a string, with fixed or free boundaries.  
Also includes transmission through an interface. 

https://www.acs.psu.edu/drussell/Demos/reflect/reflect.html  


Reflection and transmission of waves at a boundary  



Reflection from an Impedance Discontinuity 
to form standing waves 

https://www.acs.psu.edu/drussell/Demos/SWR/SWR.html  



Superposition

https://www.acs.psu.edu/drussell/Demos/superposition/superposition.html  


Superposition of waves for several cases.

https://www.acs.psu.edu/drussell/Demos/superposition/superposition.html  


Beats (show this with the two vibe tubes) 

http://www.walter-fendt.de/html5/phen/beats_en.htm  


Demos from Walter Fendt: 

http://www.walter-fendt.de/html5/phen/  


Fourier synthesizer with sound. 


http://www.walter-fendt.de/html5/phen/  


Simple Pendulum 

http://www.walter-fendt.de/html5/phen/pendulum_en.htm  


Coupled Pendula 

http://www.walter-fendt.de/html5/phen/coupledpendula_en.htm  


Spring Pendulum 

http://www.walter-fendt.de/html5/phen/springpendulum_en.htm  



Forced oscillations (resonance) 

http://www.walter-fendt.de/html5/phen/resonance_en.htm  


Coupled Pendula 

http://www.walter-fendt.de/html5/phen/coupledpendula_en.htm  


If more and more of these are coupled together, we can get waves: 


Waves 

Standing waves on string 

http://www.walter-fendt.de/html5/phen/standingwavereflection_en.htm  

https://www.acs.psu.edu/drussell/Demos/doppler/doppler.html  


Standing Longitudinal Waves 

http://www.walter-fendt.de/html5/phen/standinglongitudinalwaves_en.htm  


Doppler Effect 

http://www.walter-fendt.de/html5/phen/dopplereffect_en.htm  

https://www.acs.psu.edu/drussell/Demos/doppler/doppler.html  


Ripple Tank Simulation 

http://www.falstad.com/ripple/  

Fourier simulation (may need IE)

http://www.falstad.com/fourier/  


color-blind adapted web page of 
simulations of rectangular 2-d membrane modes

https://www.acs.psu.edu/drussell/Demos/rect-membrane/rect-mem.html