The frequency from an empty Coke bottle can be calculated using the following formula, which is named after the German scientist, Hermann von Helmholtz, who discovered and studied this phenomenon: f = In this equation, the variables are defined below: f=frequency, in hertz s = 343 meters/second (speed of sound in air) D = diameter of circular opening, in m A = area of circular opening, in m². The area of the opening is S A 2πT V x (L+0.8D) equal to (D² V = volume of bottle excluding the neck region, in m³ L= length of neck region, in m The constants 2 and 0.8 can be considered exact (with an infinite number of significant digits). Using the measurements provided below, calculate the Helmholtz resonance frequency, f, in hertz (Hz). Use the Helmholtz resonance equation above. Show all your work. For this problem, you must show which digits are significant in your intermediate calculations using underlines. Round your final answer to the appropriate number of significant figures. For full credit, you must include units beside every number in all your calculations. ● Dimensions of empty Coke bottle: • D (diameter) = 1.7 cm . V (volume) = 1.00 liters. Note that there are exactly 1000 liters in 1 cubic meter (1000 L = 1 m³) L (length of neck) = 23 mm
The frequency from an empty Coke bottle can be calculated using the following formula, which is named after the German scientist, Hermann von Helmholtz, who discovered and studied this phenomenon: f = In this equation, the variables are defined below: f=frequency, in hertz s = 343 meters/second (speed of sound in air) D = diameter of circular opening, in m A = area of circular opening, in m². The area of the opening is S A 2πT V x (L+0.8D) equal to (D² V = volume of bottle excluding the neck region, in m³ L= length of neck region, in m The constants 2 and 0.8 can be considered exact (with an infinite number of significant digits). Using the measurements provided below, calculate the Helmholtz resonance frequency, f, in hertz (Hz). Use the Helmholtz resonance equation above. Show all your work. For this problem, you must show which digits are significant in your intermediate calculations using underlines. Round your final answer to the appropriate number of significant figures. For full credit, you must include units beside every number in all your calculations. ● Dimensions of empty Coke bottle: • D (diameter) = 1.7 cm . V (volume) = 1.00 liters. Note that there are exactly 1000 liters in 1 cubic meter (1000 L = 1 m³) L (length of neck) = 23 mm
Chapter2: Loads On Structures
Section: Chapter Questions
Problem 1P
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![The frequency from an empty Coke bottle can be calculated using the following formula, which is named after the German scientist, Hermann von Helmholtz, who discovered and studied this phenomenon:
\[
f = \frac{s}{2\pi} \sqrt{\frac{A}{V \times (L + 0.8D)}}
\]
In this equation, the variables are defined below:
- \( f \) = frequency, in hertz
- \( s \) = 343 meters/second (speed of sound in air)
- \( D \) = diameter of circular opening, in m
- \( A \) = area of circular opening, in m². The area of the opening is equal to \(\left(\frac{\pi}{4}\right)D^2\)
- \( V \) = volume of bottle excluding the neck region, in m³
- \( L \) = length of neck region, in m
The constants 2 and 0.8 can be considered exact (with an infinite number of significant digits).
Using the measurements provided below, calculate the Helmholtz resonance frequency, \( f \), in hertz (Hz). Use the Helmholtz resonance equation above. Show all your work. For this problem, you must show which digits are significant in your intermediate calculations using underlines. Round your final answer to the appropriate number of significant figures. For full credit, you must include units beside every number in all your calculations.
**Dimensions of empty Coke bottle:**
- \( D \) (diameter) = 1.7 cm
- \( V \) (volume) = 1.00 liters. Note that there are exactly 1000 liters in 1 cubic meter (1000 L = 1 m³)
- \( L \) (length of neck) = 23 mm
**Hints:**
- Consider converting your units to meters, meters², and meters³ before inserting them into the Helmholtz equation.
- Based on experiments I’ve performed at home, the Coke bottle hums at a frequency between 100 and 200 Hz. If your answer is not within this range, please check your calculations.
**Graph/Diagram Explanation:**
The image includes a diagram of an empty Coke bottle labeled with dimensions:
- \( D \) is marked as the diameter of the opening at the top.
- \( L \) is marked as the length of the neck](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F56b9ddaf-a5b9-4606-96af-f9c7010351c4%2F9735d985-d538-4aab-9973-ef2d7d116b6a%2Fsoybt5_processed.png&w=3840&q=75)
Transcribed Image Text:The frequency from an empty Coke bottle can be calculated using the following formula, which is named after the German scientist, Hermann von Helmholtz, who discovered and studied this phenomenon:
\[
f = \frac{s}{2\pi} \sqrt{\frac{A}{V \times (L + 0.8D)}}
\]
In this equation, the variables are defined below:
- \( f \) = frequency, in hertz
- \( s \) = 343 meters/second (speed of sound in air)
- \( D \) = diameter of circular opening, in m
- \( A \) = area of circular opening, in m². The area of the opening is equal to \(\left(\frac{\pi}{4}\right)D^2\)
- \( V \) = volume of bottle excluding the neck region, in m³
- \( L \) = length of neck region, in m
The constants 2 and 0.8 can be considered exact (with an infinite number of significant digits).
Using the measurements provided below, calculate the Helmholtz resonance frequency, \( f \), in hertz (Hz). Use the Helmholtz resonance equation above. Show all your work. For this problem, you must show which digits are significant in your intermediate calculations using underlines. Round your final answer to the appropriate number of significant figures. For full credit, you must include units beside every number in all your calculations.
**Dimensions of empty Coke bottle:**
- \( D \) (diameter) = 1.7 cm
- \( V \) (volume) = 1.00 liters. Note that there are exactly 1000 liters in 1 cubic meter (1000 L = 1 m³)
- \( L \) (length of neck) = 23 mm
**Hints:**
- Consider converting your units to meters, meters², and meters³ before inserting them into the Helmholtz equation.
- Based on experiments I’ve performed at home, the Coke bottle hums at a frequency between 100 and 200 Hz. If your answer is not within this range, please check your calculations.
**Graph/Diagram Explanation:**
The image includes a diagram of an empty Coke bottle labeled with dimensions:
- \( D \) is marked as the diameter of the opening at the top.
- \( L \) is marked as the length of the neck
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