What two factors will most likely change the speed of a mechanical wave?

Speed of mechanical wave (sound wave) is given by the formula

here we can say that speed of sound wave depends on two factors

1). E = elasticity

2). = density

also we can have the string wave speed given by the equation as

here we can say it will depends on

1). T = tension in the string

2) = linear mass density

Also we will have the speed of sound in gases given as

here it depends on two factors as

1). = Type of gas

2). T = temperature of gas

it's when something is going so fast it makes a loud noise, breaking the sound barrier, for example: a jet makes a loud noise, not only cause of the jet but because they reached a point where they went so fast that you can year the noise from various parts, kinda like a police car, lets say the car was going   so fast that you hear the siren of the cop car right next to you, but the car is probably a mile a way, it's cos the siren was next to you a few seconds if you understand me