Why Does the Carrier Wave Amplitude Have to Be Largest in Amplitude Modulation

Strictly speaking it does not . However if it is not then demodulation gets much trickier and some would argue that the modulation is no longer purely amplitude modulation.Lets consider an equation for an AM carrier modulated with a single sinewave. Lets consider that we perform the modulation by multiplication. $$Y = (asin(omega_st)b)sin(omega_ct)$$Where $omega_s$ is the angular frequency of our signal and $omega_c$ is the angular frequency of our carrier.Now lets bash that equation around a bit to find the frequency components of our AM signal.$$Y = asin(omega_st)sin(omega_ct)bsin(omega_ct)$$$$Y = frac12a(cos(omega_st-omega_ct)-cos(omega_stomega_ct))bsin(omega_ct)$$So our modulated signal consists of three frequencies, a carrier with an amplitude of $b$ and two sidebands eavh with an amplitude of $frac12a$. So our attention turns to what the values of a and b should be. If $a leqslant b$ then we are modulating the amplitude of the carrier. At the high peak of the signal the amplitude of the carrier will be ba while at the low peak of the signal the amplitude of the carrier will be b-a. But if $a gt b$ then $asin(omega_st)b$ will drop below zero for part of the signal cycle. The amplitude of a signal cannot drop below zero, so with our multiplier based modulator what instead happens is the phase reverses. We will call this an over-modulated signal. It takes quite an advanced modulator to actually implement this reversal properly, simpler modulators may instead saturate destroying information. Ok so now we want to demodulate the signal, how do we do that? Turns out there are basically two methods. The first is envelope detection. Basically we rectify the signal and look for the peaks. The key observation with this type of demodulation is it does not care about the frequency or phase of the signal only it's amplitude. In other words the result of demodulation is roughly.$$D = |asin(omega_st)b|$$If $a leqslant b$, we have our signal with a DC offset, but if $a > b$ then parts of our signal will be inverted. So we cannot use envelope detection to correctly demodulate an over-modulated signal.The other method is coherent demodulation. In this demodulation technique we multiply the signal by the carrier again. Then filter off the high frequency components.$$D_mathrmuf = (asin(omega_st)b)sin(omega_ct)sin(omega_ct)$$$$D_mathrmuf = (asin(omega_st)b)frac1 - cos(2omega_ct) 2$$$$D = (asin(omega_st)b)frac12$$So coherent demodulation can demodulate an over-modulated signal.However in practice coherent demodulation is much harder to implement than envelope detection, because the frequency and phase of the carrier used for demodulation must match up with that used for modulation. Since the demodulator does not generally have an exact copy of the carrier used for modulation it must implement a system to estimate it

1. Pet carrier measurement and should they share or each have their own?

Airline-style crates are a great investment! Each puppy should have their own, and you should be able to "guestimate" base on their breed(s) the sizes that they will need. I would guess that both would do great in a Vari-Kennel "medium" or equivalent, though the Beagle may do well in one size smaller ("small"). What we've done with all of our dogs - for their safety and our peace of mind - is to make the crate like their bedroom and a normal part of the routine. Our three dogs all sleep in their crates at night, are crated when they must be left alone, and are fed in their crates (except for the one whose health condition requires an elevated dish). When we travel or attend a dog show or other event, we take their "bedroom" with us which allows us to keep them safe and happy in the car, ringside, and in a hotel room if we need to step out. Each of our dogs has a thrift-store purchased washable blanket in their kennel that is laundered when needed, and we clean the plastic crate by hosing it down (if it's really bad) or wiping it down with a mild cleaner or a damp cloth. The crates are placed next to each other so the dogs can hear, smell, and (through the side vents) see each other - this keeps the rescue dog's separation anxiety at a minimum and makes "crating up" and getting everyone up in the morning really easy. Because they eat in their kennels, their own space, the other dogs and the cats do not pester the slow eater. Good luck with your new pups! Thanks for doing your research and for choosing rescue!

2. Why is it so hard to build an aircraft carrier?

have you ever even seen one in real life? they are pretty damn big, so of course they cost a lot of money to build,operate, and maintain and you can not just snap them together in half an hour like a lego set or something

3. How Does An Aircraft Carrier Float?

It floats because the volume of water it displaces is equal to its weight. So if you go to the Plimsoll line or load line, then if the volume inside the ship around and below that line is equal to the weight of water of that volume, it will equal the weight of the ship. At around 62.4 pounds per cubic foot that will translate to the volume if you use 62. 4 pounds converted to tons and it will give you cubic feet of displacement