# Is this true about waves?

Once in a discussion with my teacher about mechanical waves he told that in a system containing a wave generator and reflector, the node number $$n$$ between these two things will be always integer. Like this,

Then I said if the wave starts to propagate and I bring the reflector to a $$2m$$ distance, then the wave will squeez (make its wavelength short or long) enough to make integer numbered nodes.

However I don't see any logic in this. If one wave starts propagating then how can it change its wavelength in its path? So is it right or wrong?

• I have mistaken in the second part of second picture. The wave is reflected and is coming backwards. – Theoretical Jan 13 at 16:11
• It depends on the wave generator, it depends on what 'always' means. Nevertheless, the number of nodes is always an integer (including 0)---what does a non-integer number of nodes look like? Can you have 7/22 of a node? – JEB Jan 13 at 17:04

It is not true that if you move the reflector here and there you would get standing waves. They can only happen if the length between the reflector and your generator is integer half wavelengths ($$L=n\lambda/2$$). The condition here is that $$n$$ has to be an integer (because when $$n$$ is defined, it really means the number of nodes, which should be a positive integer).

In your example, in the first set of diagrams, the $$n=3$$. But in your second set of diagrams, it obviously can't be the same. As your wave can not squeeze or do that sort of thing, and because of what I wrote in the first para - only half integer wavelengths can ever fit in between the reflector and the wave generator. Anything else cannot contribute to the formation of standing waves. In diagram 2, the total length between the reflector and the wave generator is equivalent to $$\lambda$$ (metres), and $$n=2$$ (You luckily can find an integer value in this case if you use the same formula that I listed above, that is, $$n=2L/\lambda$$, with L being different as you have reduced your the distance by 1 m.

• Can you elaborate your last partt un which you wrote "In diagram 2,....... corresponds to $n=2$? What do you really mean by it can't understand. – Theoretical Jan 14 at 7:43
• So $n$ will be $\frac {2\times 2}{1.5}?$ How is this an integer? – Theoretical Jan 14 at 16:00
• Your wavelength will be 2 units, not 1.5. As $\lambda = 2(3)/3$ – KV18 Jan 14 at 16:44
• So if I reduce my distance $.5 m$ then it won't be integer??? – Theoretical Jan 14 at 17:02
• No. You get a decimal 0.5 or so in your result for the number of nodes, which does not make sense as you can't see 2.5 points can you? – KV18 Jan 14 at 17:09