Is My Wave Superposition Calculation Correct?

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The discussion centers on verifying the calculation of the resultant wave from two given waves, y1=3sin(kx-wt) and y2=4cos(kx+wt). The user claims to have derived the resultant wave as y=7 cos(wt+45) sin(kx+45) and seeks confirmation of its accuracy. They explain their method involved adding amplitudes and applying trigonometric identities to combine the sine and cosine functions. The conversation emphasizes the need for feedback on the correctness of the calculation. The user remains eager for clarification on their result.
moham_87
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could anyone check that for me please

Hiiiiiiiiiii everyone
I've these two waves
y1=3sin(kx-wt)
y2=4cos(kx+wt)
I need to find the resultant wave (y1+y2)
I got that answer:

y= 7 cos(wt+45) sin(kx+45)
is that right?? please if not give me a hint

bye bye
 
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How about giving us some ideas as to HOW you got that and why you think it might be right.
 
here is my EFFORTS

I added the amplidtude mathematically
then using trigonometric rules i added the two "sin" and "cos" functions

sin(a)+sin(b)=sin((a-b)/2)cos((a+b)/2)...or something like that

BYE BYE...i still need to know if my answer is true

bYYyYyyyYYyYYyYE
 
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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