This is a story of HaHa, going to Psy's concert and encountering some physics problems, regarding sound intensities and power.

1. Ai Xin Wang
#14710140
LO 4- Textbook section:15-6

2. HaHa is a big fan of Psy. He went to Psy’s concert
over Korea in summer 2014. It was the most
memorable night in HaHa’s life. He arrived early
that night (3 hours prior to the concert) and
waited outside of the concert place(500m away
from the performing stage), along with other
fans.

3. While he was waiting, he heard Psy
rehearsing inside. According to his
knowledge from Physics 101, he knows
such sound system typically has a total
power of 50 kW, but why did it sound
so light from where he was?

4. Then, he realized it was due to his far away distance
(500m) from where the sound was producing. If he was
standing 1m from the speakers of the concert, the
sound intensity would have been 250000 times higher
than 500m away.
Solution
Equation: P=I4π(r^2)
A= sound intensity 1 meter away from the speaker
B= sound intensity 500 meters away from the speaker
P= IA4π(1^2); P= IB4π(500^2)
Since the total power radiated is the same, we can set the two equations
equal to each other
IA4π(1^2)=IB4π(500^2)
IA/IB= 4π(500^2)/4π(1^2)=250000

5. After waiting for 5 hours, the concert finally began. Psy
first performed his most famous song, “Gangnam Style”
as expected. And HaHa who had a VIP ticket, got to
dance with Psy only 20 meters away from him. Knowing
the sound intensity was 0.35W/m^2, HaHa suddenly
wanted to know what was the power radiated to bring
such high sound intensity.
HaHa: What is the
power radiated?
Hummmm

6. Solution
Equation: P=I4πr^2
P= (0.35W/m^2)(4π20^2)
=1759 W

7. During the concert, he felt desperate and sneaked into the
washroom backstage. Surprisingly, he felt the music to be
so much lighter (at least 5 times lighter) in the backstage.
Then he soon realized that the speakers were not isotropic
point sources, meaning the power do not radiate uniformly
in all directions. They direct the output toward the
audience only. That also means the real power radiated
should be 5 times lesser than the power radiated
isotopically.
Solution:
The real power radiated: 1759 W/ 5= 352 W

8. After the concert, considering his
health, HaHa wanted to know if the
concert had an effect on his hearing.
Solution
Equation: β(I)= 0 dβ + 10log10 ( I/I0 )
β= 0 dβ + 10 log (0.35 W/m^2÷10^-12W/m^2)= 115 dβ
The sound intensity was really close to 120, which is the level that causes hearing loss.
Though it wouldn’t cause hearing damage for short period of time, long term
exposure under such high sound intensity certainly harms ears.