Car trouble: Caused by rusted muffler?

A few weeks ago, I was in my car and pulling out of my apartment complex when I thought I heard an airplane flying overhead. I soon realized my car was making the sound, but only when first accelerating. Once the car reached approximately 25 mph, the noise stopped.

I thought the issue might be low tire air pressure, so I checked my tires. Air pressure was normal.

I thought the issue might be a part dragging on the ground. When my car was stopped, I looked underneath and nothing seemed to be hanging low.

The sound has continued up until 25 mph for the last few weeks, but today, when pulling out of another parking lot, my car made an awful high-pitched squeal. The sounds stopped a minute later, but the experience was unsettling and the rumbling sound from before persisted while below a certain speed.

When I arrived home today, I looked under my car again and noticed my car’s muffler was rusted:

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Is it likely a rusted muffler is the culprit? If so, what would be the least expensive (yet still safe) solution? I’ve been unemployed for the better part of two years and the job I work now only lasts until the project ends.

Any advice is greatly appreciated.

UPDATE: I took my car to a local auto repair shop and, while my muffler indeed looks rough, it is not leaking. The problem causing the awful sounds is instead with the rear brakes. It doesn’t take a mechanic to know that’s not good.

This is very bad news as the ballpark estimate for repairing the issue is considerably more than the cost of installing a new muffler.