Question

If the intensity of sound is increased by a factor of 30

Answer 1

Let I and I' be the old and new intensity of sound. Then, according to question
I
'
=
20
I
⇒
I
'
I
=
20


We know that
β
=
10
log
e
(
I
I
0
)





(
in

dB
)

Then change in sound level can be given as
Δ
β
=
β
2
-
β
1
=
10
log
e
(
I
'
I
0
)
-
10
log
e
(
I
I
0
)
=
10
log
e
(
I
'
I
)
⇒
Δ
β
=
10
log e
(20)≃
10×3=30

dB

Answer 2

Let I and I' be the old and new intensity of sound. Then, according to question
I
'
=
20
I
⇒
I
'
I
=
20


We know that
β
=
10
log
e
(
I
I
0
)





(
in

dB
)

Then change in sound level can be given as
Δ
β
=
β
2
-
β
1
=
10
log
e
(
I
'
I
0
)
-
10
log
e
(
I
I
0
)
=
10
log
e
(
I
'
I
)
⇒
Δ
β
=
10
log e
(20)≃
10×3=30

dB