OK ...let me try...I understood this concept fairly well...
I am assuming that you are familiar with the meaning of the fundamental frequency, standing waves and harmonics in general. I'll chip in a few explanations...
Every object has a natural frequency...this is the frequency which if matched by an external source will cause resonance in the object. Resonance can be looked upon as constructive interference of the objects natural frequency which causes maximum possible amplification ( this amplification can go on endlessly except for the fact that energy is lost at a point)
To understand harmonics you must understand nodes and standing waves. A standing wave is a wave that results when two waves (lets say sine waves) of equal frequency and wavelength moving in opposite directions interfere. There is an excellent diagram in the EK book that explains it....At the points where there is maximum constructive interference you have an antinode (this is the point on the standing wave where Amplitude is maximum). On the other hand the node is where there is no displacement and the molecules in the medium (lets sat a rope) at this point are stationary.
When a Standing Wave is formed it will seem as if the wave is simply standing in a position (which is of course not entirely true as there are two waves interfering with each other to form the standing wave in the first place)
Anyway...In question 704 EK 1001, the string is tied (guitar string) at both ends. The ends become nodes by default if the strings ever form a standing wave. This is because the positions where the string is tied does not/can not move. The ends of the string are also points from where the transverse waves will reflect and move back along the string. At the right frequency the reflecting wave causes interference with the original wave to form a standing wave. But there could be a series of standing waves with an increasing no. of complete wavelengths on the string.
When the ends are two nodes: there could be half a wavelength equal to the length of the string (this would be the first harmonic or fundamental frequency), the second harmonic would be one full wavelength, the third one and a half wavelength and so on....multiples of lamba/2.
You need to visualize this concept of two nodes. If you realize that in a single sine wave, one complete turn of 360 degrees results in the base being touched three times (This is a crude way of explaining this but I think it will work).
...A.................X...................B......................Y..................C
The diagram above shows what i mean by the 3 points (A,B,C).
These three could be nodes on a standing wave. the least number of nodes we have on our string tied at two ends is two which according to the diagram above is have a wavelength.
SO FROM HERE COMES THE EQUATION L= n*(lambda)/2, n=1,2,3,4
The situation in question 705 Ek 1001 is different.
A tube that is open at one end has one node (the closed end) and one open end that would be an antinode.
To start a harmonic series with such a setup will require that we consider 1/4th of the wavelength ( the portion of the wave between A and X) so that we can get a perfect node and an antinode in ensuing standing wave.
Subsequently, the second harmonic would again require an antinode at one end and a node at the other other which would be represented by 3/4th of the wavelength (A to Y)
As you can see, in this case the equation changes and L= n*(lambda)/4 and n = 1, 3, 5 and so on....
L of course is the length of the tube or the string....
I dont know if this is a good explanation. I understand it this way and I guess a physicist could point out many mistakes in the way its been explained...but if it works for you then my purpose is solved
