Question

for a standing wave, why are there more resonance cases as frequency increases?

Answer 1

As frequency increases, wavelength goes down and there are more probability if nothing else that the nodes will be aligned with the necessary end points of the standing wave and thus resonate. That's by 15 cent answer.

Answer 2

what do you mea if nothing else? i believe that there is a typo

Answer 3

*my

Answer 4

*mean

Answer 5

I mean that at 10:30 at night after 15 seconds of thought, this is the first reason for why higher frequency waves are more resonant comes into my head.

So I do mean "if nothing else, this is one casual factor".

Answer 6

thank you for making me seem like an idiot, it is 11:42pm where i am at. i have been sleeping at 1 for the past 3 weeks, this is the 4th. waking up at 6 lol life of a college student

Answer 7

I'm not sure I followed all that, but the more I think about it, the more I think this is the answer. Part of the ambiguity in my mind is what "resonance CASES" means in your question.

But I think its clear that whether the standing wave be acoustic or EM or water or whatever it may be, the higher the frequency of a traveling wave meeting a cavity space--such as the sound box of a violin--the more opportunities it has has to resonate in that space.

Answer 8

Well, lamda is related to length, the shorter the length, the shorter the lamda, the higher the frequency. Keeping that in mind, we know the relation v=1/f*λ=v, therefore at higher frequencies, we will have a lower lamda and more resonances. The higher the frequency, the more harmonics are produced.
does this make sense?

Answer 9

Lambda is wave length, yes.

But it's not true that the higher the frequency, there are more harmonics.

Answer 10

well f=v/l
l=2L/n

Answer 11

i guess the harmonics part is wrong lol

Answer 12

so basically, there is a higher resonance at higher frequencies, because a higher chance of resonating in an empty space so between two nodes? but why is it that the higher the frequency, it kind of seems a little vague to me

Answer 13

like what does a higher frequency have to do with the cavities?

Answer 14

i think it is because, a high frequency means a low wavelength, and a low wavelength is lower with the larger the value of n is.

Answer 15

so then there will be more harmonics, and like you said higher chance of resonating in between two nodes.

Answer 16

Suppose a wave incoming into a resonator has wave length lambda, and the reaches the far end of the resonator, a distance d, and bounces back. The total distance covered is
2d
and that must be an integer multiple of lambda, otherwise the wave will destructively interfere with itself. I.e., we have
\[ 2d = n \lambda \]
where n is an integer.
Now rearranging and using the fact that \( v = \lambda f \), we have that the frequency must be
\[ f = \frac{nv}{2d} \]

Answer 17

correct

Answer 18

There is therefore a lowest frequency f that can resonate, that which we call often the fundamental; we have for n = 1
\[ f = v/2d \]
But for every multiple about that there is another resonate frequency.

Answer 19

So returning to the question "why are there more resonance frequencies?" if we take the "more" here to mean "there are yet more of them" vs. "their incidence is higher", then we have the explanation. If you want the "incidence is higher" meaning of more, then the argument is less obvious.

Answer 20

its part of my lab for a theory portion, im just finding it hard to get my head around it. basically it asks:
explain why there are 3 cases of resonance when f=500Hz, 4 cases of resonance when f=700Hz and 6 cases of resonance when f=1000Hz?

Answer 21

my understanding of this was why is that as frequency increases we have more resonances.

Answer 22

Ok, that is the second meaning of more.

But you need to be precise! What exactly is the set up here?

Write the exact question and repost it. I'll look at it tomorrow morning.

Answer 23

i have to hand it in tomorrow morning :S but i cant type up a precise quetions it is a lab. basically we had a tube a resonator and every time with moved the cork upwards toward a tube a sound wpould change whne it changed then tahts when we knew it was a resonance frequency. and measured the length with a meter stick taped to the tube.

Answer 24

why is there a higher incidence?