Phase Difference for Interference of Traveling Waves on a Stretched String

AI Thread Summary
The discussion focuses on determining the phase difference required for two identical traveling waves on a stretched string to produce a resultant amplitude of 1.3 times the common amplitude. The equation used indicates that the amplitude of the combined wave is given by 2ymcos(1/2Φ), leading to the calculation of Φ as approximately 1.7 radians. The user seeks clarification on expressing this phase difference as a fraction of the wavelength, noting that a full wavelength corresponds to 2π radians. The conversation highlights the importance of careful calculations, especially when converting radians to fractions of a wavelength. Overall, the thread emphasizes understanding wave interference and phase relationships in wave mechanics.
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Homework Statement



What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.3 times that of the common amplitude of the two combining waves? Express your answer in (a) degrees, (b) radians, and (c) as a fraction of the wavelength.

Homework Equations



Same frequency and amplitudes results in:

y(x,t)=2ymcos(1/2Φ)sin(kx +/- wt +.5Φ)


The Attempt at a Solution



Amplitude of resultant wave = 2ymcos(1/2Φ)

2ymcos(1/2Φ)=2.3ym

solving for Φ :

2arccos(1.3/2)=Φ which is 1.7rad

However, I'm not sure how to express this in terms of the wavelength.
 
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Just looking for fraction of the wavelength. A whole wavelength would be 2*pi rad worth of phase, yes?
 
That's what I had thought. Actually, I had done: 1.7/2pi, but I didn't put parenthesis around 2pi on my calculator. Jeez. Well, I guess the semester just started. Thank you lewando!
 
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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