How Do You Calculate Wave Properties and Tension in a String?

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To calculate wave properties and tension in a string, the mass of the string (0.02 kg) and its length (25 m) are essential. The wave frequency is given as 3 Hz, which is crucial for determining wave velocity and wavelength. The relationship between wave speed, tension, and mass per unit length can be explored using formulas that incorporate these variables. Understanding these relationships will aid in calculating the amplitude, wavelength, velocity, and tension in the rope. For detailed guidance, refer to the provided HyperPhysics link.
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A string has a mass of 0.02 kg that's 25 m long. The wave has a frequency of 3 Hz. Find the amplitude, wavelength, and velocity of the wave and tension in the rope. Would really appreciate any help on this question. Having a terrible time with it.
 
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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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