Always appreciate your quality videos. In this instance, does the equation only hold if the angles are small, which was our assumption in the derivation. Thank you.
yes, however the analysis doesn't indicated how small. For large amplitudes there would be another term (non-linear wave equation) that would need to be included. For waves on a string the basic wave equation seems to do a pretty good job for larger amplitudes which tells me that the non-linear terms are probably small.
At 5:17 -- I understand that you used the small angle approximation assuming that both theta1 and theta2 would be equal along line segments bounded by delta x. My question is how exactly were you able to use the small angle approximation for ALL points along the string. Take for instance the points between any trough and peak, how would you be able to apply the approximation to those points where theta1 and theta2 would (at least by first glance) not be small enough to having sin (theta) = tan (theta)?
Why is delta(m) = mudelta(x)? Shouldn’t it be mudelta(s) which is the segment along the string? Or a we assuming since theta is small delta(s) and x are the same
You can expand trig function and keep only terms up to linear terms. Others terms will be small if thetas are small. So cos theta is approx 1 and sin theta terms are approx theta.
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That's just how physicists do their thing. I'm pretty sure this only works for an idealized model. A lot of the proofs I've seen come from idealized models, and the formulas that come out are pretty reliable.
Nice derivation. I have watched a few other derivations and yours seemed to make the most sense to me. Appreciate it. Thank you.
Glad it was helpful!
you explained one by one clearly. Thank you!
Since tension is unofirm and theta 1 equals theta 2 then sum of forces over Y equals zero not ma
Always appreciate your quality videos. In this instance, does the equation only hold if the angles are small, which was our assumption in the derivation. Thank you.
yes, however the analysis doesn't indicated how small. For large amplitudes there would be another term (non-linear wave equation) that would need to be included. For waves on a string the basic wave equation seems to do a pretty good job for larger amplitudes which tells me that the non-linear terms are probably small.
elaborate explanation, thanks bro
You are welcome
Very helpful thank youuu
At 5:17 -- I understand that you used the small angle approximation assuming that both theta1 and theta2 would be equal along line segments bounded by delta x. My question is how exactly were you able to use the small angle approximation for ALL points along the string. Take for instance the points between any trough and peak, how would you be able to apply the approximation to those points where theta1 and theta2 would (at least by first glance) not be small enough to having sin (theta) = tan (theta)?
You are making small angle approximation for 2 points that are infinitesimally close to each other.
naah bro explained exponentially better than my proff. 😭
Thanks so much, really appreciate it🙌
Why is delta(m) = mudelta(x)?
Shouldn’t it be mudelta(s) which is the segment along the string?
Or a we assuming since theta is small delta(s) and x are the same
Yes
its bcoz mu(the mass density)= del m(mass)/del x(displacement)
THANKS
You're welcome!
Thank you! You are a beast
What's the purpose of the small angle approximation here? And why do we assume theta is a relatively small angle?
To make the equation easier , you could find this for large angle but irl small angle works just fine
En büyük müsün bilmiyorum ama çok büyüksün ninja abi.
why do we use theta1=theta1 in the horizontal direction but not in the vertical direction?
You can expand trig function and keep only terms up to linear terms. Others terms will be small if thetas are small. So cos theta is approx 1 and sin theta terms are approx theta.
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After this much approximation , I think the equation is literally useless.
That's just how physicists do their thing. I'm pretty sure this only works for an idealized model. A lot of the proofs I've seen come from idealized models, and the formulas that come out are pretty reliable.
welcome to physics
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