Solutions

• is a wave because (1.) it can be rewritten as where and (2.) the derivatives satisfy the wave equation.
• is a wave because (1.) it can be rewritten as where and (2.) the derivatives satisfy the wave equation.
• is not a wave. You can't rewrite it in the forms p(x,t)=f(x-ct) or p(x,t)=g(x+ct). Its derivatives don't satisfy the wave equation.
• p(x,t)= 1.0 is a little bit tricky because its derivatives do satisfy the wave equation, but it can't obviously be rewritten in the forms p(x,t)=f(x-ct) or p(x,t)=g(x+ct). However, since we can rewrite it as p(x,t)= 1. + 0*(x-ct), it does represent a wave.