Distance traveled by a knot in a string ungergoing wave motion.

[new324]

Once again, I've become stuck on the easiest problem in the chapter (though I'm steamrolling the tougher ones). I just can't get the concept of this one down I guess. Thanks for any help.

A 4 Hz wave with amplitude 12 cm and a wavelength 30.0 cm travels along a stretched string. (a) how far does the wave travel in 5 seconds and (b) how far does a knot on a string travel in the same amount of time.

Well (a) is pretty cut and paste. Using v=λf we find v=1.2 m/s. 5*v= 6 m. I'm not sure how to go about calculating the distance the knot travels. I'm not sure if I should think about it as as a circular motion (like a cork in a water wave) or if its just a simple harmonic motion (up and down over and over) or what. Any hints to get me started? Thanks!

 

[Doc Al]

I'm not sure how to go about calculating the distance the knot travels. I'm not sure if I should think about it as as a circular motion (like a cork in a water wave) or if its just a simple harmonic motion (up and down over and over) or what.

Water waves are a combination of transverse and longitudinal motion. This wave on a string is not as complicated--it's a pure transverse wave. You are on the right track thinking of simple harmonic motion.

 

[new324]

Great, thanks Doc Al!