Sound waves in different mediums
- 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