Wave Equation Derivation - Transverse Waves on a String

Physics Ninja looks at the derivation of the wave equation for a wave on a string.

[@millenniumcreativestudio5081]

After this much approximation , I think the equation is literally useless.

[@5gallonsofwater495]

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.

[@laddu-jillu3583]

welcome to physics

[@sirwinston2368]

Nice derivation. I have watched a few other derivations and yours seemed to make the most sense to me. Appreciate it. Thank you.

[@PhysicsNinja]

Glad it was helpful!

[@griffithfimeto3387]

Since tension is unofirm and theta 1 equals theta 2 then sum of forces over Y equals zero not ma

[@kina4288]

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.

[@PhysicsNinja]

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.

[@edoardo_rubino]

why do we use theta1=theta1 in the horizontal direction but not in the vertical direction?

[@PhysicsNinja]

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.

[@mrslave41]

11:01 “previous” i didn’t watch. now i’m lost. please don’t tell me to watch another video now. 😢😢😢😢

[@petergoh5628]

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

[@PhysicsNinja]

Yes

[@lenops-uu7bw]

its bcoz mu(the mass density)= del m(mass)/del x(displacement)

[@ahmetcoskuntekin5956]

En büyük müsün bilmiyorum ama çok büyüksün ninja abi.

[@ecekaraa]

you explained one by one clearly. Thank you!

[@Neel-Joshii]

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)?

[@PhysicsNinja]

You are making small angle approximation for 2 points that are infinitesimally close to each other.

[@anilkumarsharma8901]

Energy is the ultimate integration of anything or anything else naturally universe ki efficiency hain maximum bot support dilva do stock market ka dividend detey rahana to sara desh aapko following karney lagega

[@mohammadibrahimahmad7546]

elaborate explanation, thanks bro

[@PhysicsNinja]

You are welcome

[@UtkarshPal23BCE047]

naah bro explained exponentially better than my proff. 😭

[@organic_antelope]

Very helpful thank youuu

[@kw4070]

What's the purpose of the small angle approximation here? And why do we assume theta is a relatively small angle?

[@theiigotriangularround4880]

To make the equation easier , you could find this for large angle but irl small angle works just fine

[@aditya_asundi]

THANKS

[@PhysicsNinja]

You're welcome!

[@anilkumarsharma8901]

Energy is the ultimate derivative of anything or anything else naturally universe ki efficiency hain maximum bot support dilva do

[@IshanAtre-vv5xm]

Thanks so much, really appreciate it🙌

[@anupamkumarchauhan4987]

😂

[@Aferz]

Thank you! You are a beast