Question

You are trying to decide between two new stereo amplifiers. One is rated at 130 W per channel and the other is rated at 200 W per channel. Part A In terms of dB, how much louder will the more powerful amplifier be when both are producing sound at their maximum levels?

Answer 1

The sound level will be 1.870 dB louder.

Step-by-step explanation:

Given that,

Power = 130 W

Power = 200 W

We need to calculate the sound level

Using formula of sound level

`I_(dB)=10\log((I)/(I_(0)))`

For one amplifier,

`I_(1)=10\log((130)/(I_(0)))`...(I)

For other amplifier,

`I_(2)=10\log((200)/(I_(0)))`...(II)

For difference in dB levels

`I_(2)-I_(1)=10\log((200)/(I_(0)))-10\log((130)/(I_(0)))`

`I_(2)-I_(1)=10\log((200)/(I_(0))*(I_(0))/(130))`

`I_(2)-I_(1)=10\log((200)/(130))`

`I_(2)-I_(1)=1.870\ dB`

Hence, The sound level will be 1.870 dB louder.