Final answer:
The turns ratio for matching a 500 Ω amplifier to a low-impedance speaker is based on the square root of the impedance ratio. For increasing sound intensity, the new intensity after a 30% increase in amplitude is about 2.69x10^-5 W/m², adhering to the principle that intensity is proportional to the amplitude squared.
Step-by-step explanation:
Designing a summing amplifier to produce an output of 6A at 3V (18 W) requires consideration of the amplifier's power rate and the transformer's turns ratio. This application generally relates to audio engineering or electrical engineering. When considering a transformer to match an amplifier's output impedance of 500 Ω to a low-impedance 8-22 Ω speaker, the turns ratio of the transformer is crucial to align these impedances. The turns ratio can be calculated using the formula Z_primary/Z_secondary = (N_primary/N_secondary)^2, where Z represents impedance and N represents the number of turns in the primary and secondary coils, respectively. For mismatched impedances such as 500 Ω and 8-22 Ω, you would aim for a ratio that equals the square root of the impedance ratio to minimize power loss.
For the new sound intensity when a microphone receiving a pure sound tone is turned up, the relation between intensity and amplitude is that intensity is proportional to the amplitude squared. Thus, if the amplitude increases by 30%, the new intensity will be (1+0.30)^2 times the original intensity, leading to a new value of approximately 2.69x10^-5 W/m².