Does Amp=0 imply that a wave has 0 speed?

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A wave with an amplitude of 0 does not have any velocity, as it carries no energy and effectively ceases to exist as a wave. The trivial solution y(x,t)=0 is mathematically valid but not considered physically meaningful in the context of wave behavior. The discussion emphasizes that without amplitude, the wave cannot propagate through space. Therefore, it is concluded that an amplitude of 0 implies the absence of a wave. Understanding these principles is crucial for grasping wave dynamics in physics.
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Homework Statement



Will a wave with an amplitude of 0 have any velocity?

Homework Equations



V=F(lambda) E=kA^2


The Attempt at a Solution



I think the wave dissappears because if it carries no energy then it ceases to be a wave, but I am not sure though.
 
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You are correct :approve:.

In a little more detail the solution y(x,t)=0, is the trivial solution of the wave-equation and is not usually considered to be physically meaningful.
 
thank you.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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