Questions related to resonance/standing-waves and sound

Question

I understand resonance for a simple harmonic oscillator but not for more complex systems like standing waves.

How can I be in resonance with the normal mode in an organ pipe?

I understand that the frequency of the force acting on the system has to match the natural frequency of the column of air in the pipe. However, the force acting on the system is generating pulses of pressure waves onto the system (suppose I'm blowing air or something) and I just don't see how nodes are going to be preserved if I'm continuously sending these pulses! Namely, I'm imagining that the pulses acting on the system will disturb the nodes of whatever harmonic was present in the organ pipe. The same with a string.

Also, what exactly is a normal mode? My textbook says that standing waves can only satisfy this equation:

Longitude of rope = (lambda/2)N or anything similar that depends on the system.

The thing is I'm so darn sure I saw another type of standing wave in my physics lab, where there was a half-wavelength on one extreme of the rope that was much shorter than all the rest of half-wavelengths. In fact, I think it wasn't even a half-wavelength it was a quarter-wavelength!

Also, I keep reading that a guitar string normally vibrates according to the fundamental frequency. I've seen countless videos that demonstrate in slow-motion how the vibrating string has hundreds of crests and is clearly not in its fundamental frequency. Other sources say harmonics coexist at the same time, this makes little sense to me right now.

Finally, is the topic of waves something I will understand more clearly later on in my studies as a physics major? I've heard you study this topic a big-deal in Differential Equations. Is this true? I've only seen CalcI and CalcII.

Answer 1

Organ pipe, whistles, and the like are not fed with pulses of air. Think about it. You blow into a whistle steadily, but yet what comes out is 1000 pulses per second or so. You certainly aren't huffing 1000 times/second into the whistle.

Whistles and organ pipes are their own oscillators. You put in power in the form or moving air, and that gets turned into pulses of air coming out.

It's probably easiest to think of how a whistle works. You apply steady pressure at the nozzle end. The nozzle deliberately make a sheet of flowing air accross that little gap. The air flow continues into the body of the whistle where is swirls around and pressure builds up. Eventually pressure gets high enough so that it "breaks thru" the sheet of air running accross the opening. That lets out a burst and momentarily re-directs the sheet so that it no longer goes into the body of the whistle. The momentum of the air rushing out of the body thru the opening and a little suction created by the sheet being diverted to go outside the body of the whistle eventually creates negative pressure in the body. That brings the sheet back to flowing into the whistle, and the cycle repeats. The size of the whistle body governs how fast the pressure builds up to break-thru level, and how fast is goes down again. In other words, the larger the body, the longer each cycle takes and the lower the pitch of the sound.

Organ pipes work on quite similar principles.