How many times more intense is a 60 dB sound than a 30 dB sound ?

Question

How many times more intense is a 60 dB sound than a 30 dB sound ? (A) 1000 (B) 2 (C) 100 (D) 4

Tardigrade Admin · Accepted Answer

L =10 log 10 (I/I0) 60 =10 log 10 (I1/I0) ⇒ (I1/I0)=106 ...(i) Similarly, 30=10 log 10 (I2/I0) (I2/I0)=103 Dividing Eq. (i) by Eq. (ii), we get (I1/I2)=1000

Q. How many times more intense is a $60 d B$ sound than a $30 d B$ sound ?

$1000$

$2$

$100$

$4$

$L = 10 lo g_{10} \frac{I}{I _{0}}$
$60 = 10 lo g_{10} \frac{I _{1}}{I _{0}}$
$\Rightarrow \frac{I _{1}}{I _{0}} = 1 0^{6} ... (i)$
Similarly,
$30 = 10 lo g_{10} \frac{I _{2}}{I _{0}}$
$\frac{I _{2}}{I _{0}} = 1 0^{3}$
Dividing Eq. (i) by Eq. (ii), we get
$\frac{I _{1}}{I _{2}} = 1000$

Q. How many times more intense is a 60dB sound than a 30dB sound ?

1000

2

100

4

L=10log10​I0​I​ 60=10log10​I0​I1​​ ⇒I0​I1​​=106...(i) Similarly, 30=10log10​I0​I2​​ I0​I2​​=103 Dividing Eq. (i) by Eq. (ii), we get I2​I1​​=1000

Q. How many times more intense is a $60 d B$ sound than a $30 d B$ sound ?

$1000$

$2$

$100$

$4$

$L = 10 lo g_{10} \frac{I}{I _{0}}$
$60 = 10 lo g_{10} \frac{I _{1}}{I _{0}}$
$\Rightarrow \frac{I _{1}}{I _{0}} = 1 0^{6} ... (i)$
Similarly,
$30 = 10 lo g_{10} \frac{I _{2}}{I _{0}}$
$\frac{I _{2}}{I _{0}} = 1 0^{3}$
Dividing Eq. (i) by Eq. (ii), we get
$\frac{I _{1}}{I _{2}} = 1000$