Aerospace engineer here with a background in rocket propulsion, I’m also doing my thesis on acoustic load on launch vehicles.
The overall sound power level of a rocket can be calculated approximately by using W = 0.005*n*g*v*Isp
Where n is the number of exhaust nozzles, g is the gravitational acceleration, v is the exit velocity of the exhaust, and Isp is the specific impulse of the engine.
Larger rockets have higher exhaust velocities giving a higher overall sound power level. Converting to decibels will give a rocket like the Saturn V, which has an exhaust velocity of 2607 m/s, around 203-206 dB, which would literally kill you if you are within 3 km of the launch.
Small rockets like a hobby rocket have vastly lower exit velocities for their exhaust, on the range of 150-200 m/s. Their db value would be around 90 dB, less than a concert.
Plus the duration of burning is much different. This affects what frequency range is more prevalent. Larger rockets peak at very low frequencies, <200 Hz, while small rockets are around 6-8k Hz.
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