If you were to put – 5W speaker to 10-15W amplifier which – bass or treble will most likely damage it first?
From what I've heard and learned – boosted bass makes speaker move back and forth and if that moving energy is too big for the speaker to handle it may rip.
On the other side, boosted high frequencies generate more heat in the tweeter and it may overheat*.
One more interesting thing I found, is that it is generally better to put a 5W speaker to 10W amp instead of 5W speaker with 5W amplifier which is starting to clip because square sound waveforms (distortions) put much stress into a speaker and it starts generating heat if the clipping is too much. It may even catch on fire! While 10 clean watts give 'natural frequencies which don't put as much stress (peaks) and is easier on the speaker even though it's louder.
I think this is an interesting topic to know about.
Best Answer
As pointed out in other response, it is heat that usually causes speaker failure. I recommend this article for some additional details on physical failure mechanisms: https://sound-au.com/articles/speaker-failure.html
There are a few other details worth mentioning, since your original question asked about what frequencies are more likely to cause failure.
Low frequencies (relative to the driver in question) can often cause failure because, for a given sound power output, lower frequencies require greater cone excursion. If excursion becomes so great that the voice coil actually leaves the magnetic gap, a magnetic short is formed and lots of heat is produced. Drivers usually have a specified maximum excursion, called Xmax. Speakers designed to produce lower frequencies generally have much larger Xmax values so they can deliver sound power at low frequencies. At any rate, care must be taken to insure that the driver is not driven in such a way that the cone excursion exceeds Xmax. This can be achieved by limiting the total power delivered to the driver and/or by applying a high-pass filter to prevent low frequencies with higher associated excursions from being delivered to the driver.
For different reasons, high frequencies (relative to the driver in question) can also cause failure through a mechanism known as breakup. Basically, standing waves can develop on the cone itself. Because cones are not designed with the resulting stress in mind, this can cause the cone itself fracture.