How is the Maximum Speed of a Point on a Progressive Wave Calculated?

AI Thread Summary
The maximum speed of a point on a progressive wave can be calculated using the formula V = 2πfxA, where f is the frequency, A is the amplitude, and the factor 2π relates to simple harmonic motion. In this case, the frequency is derived from the wave speed and wavelength, resulting in a frequency of 3.0 Hz and an amplitude of 90 mm. The calculated maximum speed of point P is 1.70 m/s. There is confusion regarding the origin of the 2π factor, which is linked to the properties of harmonic motion. Understanding the general wave equation and its components is essential for grasping these concepts.
nirvana1990
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Homework Statement



Progressive waves are generated on a rope by vibrating vertically the end, P, in simple
harmonic motion of amplitude 90 mm. The wavelength of the waves
is 1.2 m and they travel along the rope at a speed of 3.6ms–1. Assume that the wave motion is not damped.

Calculate the maximum speed of point P.



The Attempt at a Solution



The actual solution is V=2(pi)xfxA
Since f=v/wavelength= 3.0 Hz and A=90x10^-3m the answer is 1.70 m/s

I don't understand why this formula is used and where the 2pi has come from. Is it to do with simple harmonic motion? I would be very grateful if someone could help with a derivation of the formula.
 
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What is the general equation of a wave?
 
equation

learningphysics said:
What is the general equation of a wave?

v=f lambda?
 
nirvana1990 said:
v=f lambda?

Have you see this equation before:

x = Acos(kx - wt)
 
oh gosh no I haven't! erm on my physics data sheet there's a similar equation: x=Acos2Pift. hmmm I'll see what comes up when I google the equation you just gave me! Thanks
 
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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