Question

A stereo speaker is rated at P1000 = 52 W of output at 1000 Hz. At 20 Hz, the sound intensity level LaTeX: \betaβ decreases by 1.3 dB. What is the power output P

Answer 1

The value of the power is
`P_c  =  38.55 \  W`

Step-by-step explanation:

From the question we are told that

The power rating
`P_(1000) =P_b=  52 \  W`

The frequency is
`f = 1000 \  Hz`

The frequency at which the sound intensity decreases
`f_k  =  20 \  Hz`

The decrease in intensity is by
`\beta  =  1.3 dB`

Generally the initial intensity of the speaker is mathematically represented as

`\beta_1 =  10 log_(10) [(P_b)/(P_a) ]`

Generally the intensity of the speaker after it has been decreased is

`\beta_2 =  10 log_(10) [(P_c)/(P_a) ]`

So

`\beta_1-\beta_2 =  10 log_(10) [(P_c)/(P_a) ]- 10 log_(10) [(P_b)/(P_a) ]`

=>
`\beta =  10 log_(10) [(P_c)/(P_a) ]- 10 log_(10) [(P_b)/(P_a) ]= 1.3`

=>
`\beta =10log_(10) [((P_b)/(P_a))/((P_c)/(P_a)) ] = 1.3`

=>
`\beta =10log_(10) [(P_b)/(P_c) ] = 1.3`

=>
`10log_(10) [(P_b)/(P_c) ] = 1.3`

=>
`log_(10) [(P_b)/(P_c) ] = 0.13`

taking atilog of both sides

`[(P_b)/(P_c) ] = 10^(0.13)`

=>
`[(52)/(P_c) ] = 10^(0.13)`

=>
`P_c  =  (52)/(1.34896)`

=>
`P_c  =  38.55 \  W`