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

Answer:

The sound level will be 1.870 dB louder.

Explanation:

Given that,

Power = 130 W

Power = 200 W

We need to calculate the sound level

Using formula of sound level

$I_{dB}=10\log(\dfrac{I}{I_{0}})$

For one amplifier,

$I_{1}=10\log(\dfrac{130}{I_{0}})$...(I)

For other amplifier,

$I_{2}=10\log(\dfrac{200}{I_{0}})$...(II)

For difference in dB levels

$I_{2}-I_{1}=10\log(\dfrac{200}{I_{0}})-10\log(\dfrac{130}{I_{0}})$

$I_{2}-I_{1}=10\log(\dfrac{200}{I_{0}}\times\dfrac{I_{0}}{130})$

$I_{2}-I_{1}=10\log(\dfrac{200}{130})$

$I_{2}-I_{1}=1.870\ dB$

Hence, The sound level will be 1.870 dB louder.