Suppose you would like to double the speed of a wave on a string. by what multiplicative factor must you increase the tension?

 The wave speed on a taut string is 
v = √(T/μ) 
where T is the tension and μ the mass per unit length of the string. 
Therefore, to double the wave speed on the string, the tension has to increase by a factor of 4. 

In your notation

1) when you rub your hands together quickly, the kinetic energy is converted to mechanical energy.2) thermal energy from the sun travels to earth as infrared waves.3) energy is transferred through the matter of space by electromagnetic waves. 4) when a match is burned, chemical potential energy is converted to thermal and radiant energy. 5) seismicwaves are caused by back and forth movement , or vibration, of an object. 6) mechanicalenergy in an engine changes thermal energy into kinetic energy to make a car move.

Well the magnitude of its acceleration related to that car starts with the oil change like when you have to change the oil in your car you have to make sure that your precious car is starting really propley and very well