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

Answer:

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

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

     $\beta_1 = 10 log_{10} [\frac{P_b}{P_a} ]$

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

       $\beta_2 = 10 log_{10} [\frac{P_c}{P_a} ]$

So

$\beta_1-\beta_2 = 10 log_{10} [\frac{P_c}{P_a} ]- 10 log_{10} [\frac{P_b}{P_a} ]$

=>  $\beta = 10 log_{10} [\frac{P_c}{P_a} ]- 10 log_{10} [\frac{P_b}{P_a} ]= 1.3$

=>  $\beta =10log_{10} [\frac{\frac{P_b}{P_a}}{\frac{P_c}{P_a}} ] = 1.3$

=>  $\beta =10log_{10} [\frac{P_b}{P_c} ] = 1.3$

=> $10log_{10} [\frac{P_b}{P_c} ] = 1.3$

=> $log_{10} [\frac{P_b}{P_c} ] = 0.13$

taking atilog of both sides

$[\frac{P_b}{P_c} ] = 10^{0.13}$      

=>$[\frac{52}{P_c} ] = 10^{0.13}$      

=>  $P_c = \frac{52}{1.34896}$

=>   $P_c = 38.55 \ W$