Question

if a car comes out of stock with a catalytic converter
then replacing the muffler to something as big as this picture below and not installing the silencer but just a straight pipe wouldn't the car sound more louder but lose more compression ?

Answer 1

To begin with, a straight exhaust system is a heavy polluter; in both noise and greenhouse gases. The resulting volume of a straight exhaust system is typically much louder than what is legal. Plus, removal of emissions equipment will send more harmful gases into the atmosphere. If you're required to pass vehicle inspections in your state, a straight pipe exhaust is an instant fail.
The common misconception is that a straight exhaust will result in increased power. This may be true in some cases, such as comparing straight exhaust to a stock muffler. But in comparison to a performance muffler, the muffler will more often than not provide more power than the straight exhaust. Furthermore, a straight exhaust system can drastically alter your power curve. The reason people tend to believe straight exhaust better is based on fallacies regarding backpressure. Yes, a straight pipe will minimize engine backpressure. However, the truth of the matter is that gasoline engines, especially those designed for trucks, require some degree of backpressure for peak performance and the broadest torque curve. This is due to the nature of the internal combustion process. In a straight exhaust system setup, backpressure is nearly eliminated. Therefore, during the exhaust and intake valve overlap, or the time when both valves are open, precious fuel escapes through the exhaust system. This is because the area of the combustion chamber surrounding the exhaust valve becomes a low pressure zone once exhaust gases are forced out of the cylinder. As the intake valve opens (and the exhaust valve is open, but in the process of closing), fuel rushes into the cylinder and is attracted to this low pressure portion of the cylinder. Since the exhaust valves have not finished closing, fuel and air exit through the valve and out the exhaust system. Hope this helps

Answer 2

Further more....
When a high performance muffler is used, enough backpressure is maintainted to eliminate the low pressure environment of the cylinder surrounding the exhaust valve, therefore keeping fuel and air from rushing out of the cylinder during the overlap time between the exhaust and intake valves. This is done while minimizing pumping losses. Less fuel in the cylinder means weaker combustion, which translates into reduced power. Additionally, mufflers are tuned to scavenge exhaust gases. This is the act of using exhaust flow to pull exhaust gases out of the cylinder at exactly the right time. There is no (or negligible) scavenging effect in a straight pipe setup.
With a straight pipe, horsepower & torque may be increased in the upper RPM range, but at the expense of significant losses in the low to mid range. For an engine that is limited to 4,500 - 5,500 rpm and is rarely operated in this range, it makes little sense to give up power in the low to mid range. For the best all around performance and fuel economy, choose a quality performance exhaust system over an open exhaust system.