How Do Phase Shifts Affect Resultant Wave Amplitude and Frequency?

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The discussion centers on determining the amplitude and frequency of two sinusoidal waves that are out of phase. The amplitude of the resultant wave is calculated using the formula A = (2A cos Phi/2), leading to an initial estimate of approximately 10m. However, there is a suggestion to check the calculator settings, specifically ensuring it is in radians mode for accurate calculations. The phase shift is confirmed to be 0.250, but there is some confusion regarding whether it should be "-0.250y" or just "-0.250" in the wave function. Overall, the key focus is on correctly applying the phase shift to find the resultant wave's characteristics.
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Homework Statement


Two traveling sinusoidal waves are described by the wave functions
y1 = (5.00m) sin[pie(4.00x - 1 200t)]
y2 = (5.00m) sin[pie(4.00x - 1 200t -0.250y)]
where x, y1, and y2 are in meters and t is in seconds.
(a) What s the amplitude of the resultant wave?
(b) What is the frequency of the resultant wave?


Homework Equations


y = (2Acos Phi/2) sin(kx- wt + Phi/2)


The Attempt at a Solution


The two waves are out of phase by 0.250
therefore A = (2A cos Phi/2)
I get the Amplitude to be 9.99 or 10m
from 2 (5.00m) .25/2
Do I need to do more for this? I know the answer but can't get there
Thanks,
Kevin
 
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Husker70 said:

Homework Statement


Two traveling sinusoidal waves are described by the wave functions
y1 = (5.00m) sin[pie(4.00x - 1 200t)]
y2 = (5.00m) sin[pie(4.00x - 1 200t -0.250y)]
where x, y1, and y2 are in meters and t is in seconds.
Is it "-0.250y" or just "-0.250" for the phase in y2?

(a) What s the amplitude of the resultant wave?
(b) What is the frequency of the resultant wave?


Homework Equations


y = (2Acos Phi/2) sin(kx- wt + Phi/2)


The Attempt at a Solution


The two waves are out of phase by 0.250
therefore A = (2A cos Phi/2)
I get the Amplitude to be 9.99 or 10m
It should be slightly lower. Was your calculator in radians mode when you calculated cos(0.25)?

from 2 (5.00m) .25/2
Do I need to do more for this? I know the answer but can't get there
Thanks,
Kevin
 
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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