Learning object for physics 101

1. Sound waves in different
mediums

2. Reference Intensities:
Water: 6.7x10-19 W/m2
Air: 10-12 W/m2

3. Question
An Indie rock group wants to host a concert for
its myriad fans but lacks the funding for
electricity to power large, power-draining 125
decibel speakers. Being former students of
Physics 101, they decide to determine whether
playing underwater will allow them to deliver
the same sound but with lower power output.

4. They are expecting a turnout that will result in
the furthest people being at 60m from the
stage.
Is it better for them to play underwater or on
the surface?

5. Hints
- You are given the reference intensity of both
water and air. What formula should you use?
- You are given the desired decibel output, is
this information important?
- You can use the logarithmic decibel equation
to solve this problem. 𝛽 = 0 𝑑𝐵 + 10log(
𝐼
𝐼0
)

6. Solution for air:
• 125 𝑑𝐵 = 0 𝑑𝐵 +
10 log
𝐼
10−12 𝑊
𝑚2
• 12.5 𝑑𝐵 = log
𝐼
10−12 𝑊
𝑚2
• 1012.5 =
𝐼
10−12 𝑊
𝑚2
• 1012.5
𝑥 10−12
= 𝐼
• 100.5
= 𝐼
• 𝐼 = 3.16 𝑊/𝑚2
Insert the numbers into
the equation
Put both sides to the power
of ten to eliminate the log
Using the properties of
exponents solve for the value, and use a
calculator the determine the number

7. Solution for water
• 125 𝑑𝐵 = 0 𝑑𝐵 +
10 log
𝐼
6.7𝑥10−19 𝑊
𝑚2
• 12.5 𝑑𝐵 = log
𝐼
6.7𝑥10−19 𝑊
𝑚2
• 1012.5
=
𝐼
6.7𝑥10−19 𝑊
𝑚2
• 1012.5
𝑥 6.7𝑥10−19
= 𝐼
• 𝐼 = 0.00000212 𝑊/𝑚2
Insert the numbers into
the equation
Put both sides to the power
of ten to eliminate the log
use a calculator the determine the number

8. Conclusion
It is much better to play underwater as the
average power output will need to be
0.00000212 W/m2 compared to air’s 3.16 𝑊/
𝑚2
Bonus: If the band can only
afford 8W of electricity how far will their
sound reach if the efficiency of speakers is 1%?

9. Bonus Solution
- 𝑃 = 𝐼4𝜋𝑟2
- P=8x0.01
- 0.08 𝑊 = (0.00000212 𝑊/𝑚2
)4𝜋𝑟2
-
0.08𝑊
0.00000212
𝑊
𝑚2 4𝜋
= 𝑟2
- 3002.9𝑚2 = 𝑟
- r = 54.8 m
The equation for distance of a sound wave
Only 1% of the power
of the speaker is transmitted as sound
Plug in the numbers, and solve
They can project sound to a total distance of 54.8 m

10. Works Cited
• http://www.privateline.com/TelephoneHistory
/speech.jpg
• http://www.submarineboat.com/images/rov/
sound%20path.jpg
• http://p4cdn4static.sharpschool.com/UserFile
s/Servers/Server_91869/Image/Band4.jpg