A Student Is Standing 8 M From A Roaring Truck Engine That Is Measured At $20 \frac{W}{m^2}$. The Student Moves 4 M Closer To The Engine. What Is The Measured Sound Intensity At The New Distance? $\square \frac{W}{m^2}$
Introduction
Sound intensity is a measure of the power per unit area carried by a sound wave. It is an essential concept in physics, particularly in the study of acoustics. In this article, we will explore the relationship between sound intensity and distance, using a real-world scenario to illustrate the concept.
What is Sound Intensity?
Sound intensity is defined as the power per unit area carried by a sound wave. It is typically measured in watts per square meter (W/m²). The sound intensity of a sound wave depends on the amplitude of the wave, which is a measure of the maximum displacement of the particles in the medium from their equilibrium position.
The Relationship Between Sound Intensity and Distance
When a sound wave propagates through a medium, its intensity decreases with distance from the source. This is because the energy of the sound wave is spread out over a larger area as it travels further away from the source. As a result, the sound intensity at a given distance from the source is inversely proportional to the square of the distance.
Mathematical Representation
The relationship between sound intensity (I) and distance (r) can be represented mathematically as:
I ∝ 1/r²
where I is the sound intensity and r is the distance from the source.
Real-World Scenario
Let's consider a student standing 8 m from a roaring truck engine that is measured at 20 W/m². The student moves 4 m closer to the engine. What is the measured sound intensity at the new distance?
To solve this problem, we can use the mathematical representation of the relationship between sound intensity and distance. Since the student moves 4 m closer to the engine, the new distance from the engine is 8 m - 4 m = 4 m.
Using the mathematical representation, we can calculate the new sound intensity as follows:
I₂ = I₁ * (r₁/r₂)²
where I₂ is the new sound intensity, I₁ is the initial sound intensity (20 W/m²), r₁ is the initial distance (8 m), and r₂ is the new distance (4 m).
Plugging in the values, we get:
I₂ = 20 W/m² * (8 m/4 m)² I₂ = 20 W/m² * 4 I₂ = 80 W/m²
Therefore, the measured sound intensity at the new distance is 80 W/m².
Conclusion
In conclusion, the relationship between sound intensity and distance is inversely proportional, meaning that the sound intensity decreases with distance from the source. Using a real-world scenario, we have demonstrated how to calculate the new sound intensity at a given distance from the source. This concept is essential in understanding how sound waves propagate through a medium and how their intensity changes with distance.
Applications of Sound Intensity and Distance
The concept of sound intensity and distance has numerous applications in various fields, including:
- Acoustics: Understanding the relationship between sound intensity and distance is crucial in the design of sound systems, such as speakers and microphones.
- Noise Pollution: Knowing how sound intensity changes with distance is essential in assessing the impact of noise pollution on human health and the environment.
- Medical Applications: Sound intensity and distance are used in medical imaging techniques, such as ultrasound and MRI.
Frequently Asked Questions
- What is the relationship between sound intensity and distance? The relationship between sound intensity and distance is inversely proportional, meaning that the sound intensity decreases with distance from the source.
- How do you calculate the new sound intensity at a given distance from the source? You can use the mathematical representation I ∝ 1/r² to calculate the new sound intensity.
- What are the applications of sound intensity and distance? The concept of sound intensity and distance has numerous applications in acoustics, noise pollution, and medical imaging techniques.
References
- [1]: "Acoustics: An Introduction to Its Physical Principles and Applications" by Allan D. Pierce
- [2]: "The Physics of Sound" by Lawrence E. Kinsler
- [3]: "Sound and Vibration" by David G. Leventhall
A Student is Standing 8 m from a Roaring Truck Engine: A Q&A on Sound Intensity and Distance =====================================================================================
Introduction
In our previous article, we explored the relationship between sound intensity and distance, using a real-world scenario to illustrate the concept. In this article, we will answer some frequently asked questions related to sound intensity and distance.
Q&A
Q1: What is the relationship between sound intensity and distance?
A1: The relationship between sound intensity and distance is inversely proportional, meaning that the sound intensity decreases with distance from the source.
Q2: How do you calculate the new sound intensity at a given distance from the source?
A2: You can use the mathematical representation I ∝ 1/r² to calculate the new sound intensity. This means that the new sound intensity is equal to the initial sound intensity multiplied by the square of the ratio of the initial distance to the new distance.
Q3: What are the applications of sound intensity and distance?
A3: The concept of sound intensity and distance has numerous applications in various fields, including:
- Acoustics: Understanding the relationship between sound intensity and distance is crucial in the design of sound systems, such as speakers and microphones.
- Noise Pollution: Knowing how sound intensity changes with distance is essential in assessing the impact of noise pollution on human health and the environment.
- Medical Applications: Sound intensity and distance are used in medical imaging techniques, such as ultrasound and MRI.
Q4: How does the sound intensity change when the distance from the source is doubled?
A4: When the distance from the source is doubled, the sound intensity decreases to one-quarter of its original value. This is because the sound intensity is inversely proportional to the square of the distance.
Q5: What is the effect of increasing the sound intensity on the distance from the source?
A5: Increasing the sound intensity will decrease the distance from the source at which the sound intensity is measured. This is because the sound intensity is inversely proportional to the square of the distance.
Q6: Can you give an example of how to calculate the new sound intensity at a given distance from the source?
A6: Let's consider a student standing 8 m from a roaring truck engine that is measured at 20 W/m². The student moves 4 m closer to the engine. To calculate the new sound intensity, we can use the mathematical representation I ∝ 1/r². Plugging in the values, we get:
I₂ = I₁ * (r₁/r₂)² I₂ = 20 W/m² * (8 m/4 m)² I₂ = 20 W/m² * 4 I₂ = 80 W/m²
Therefore, the measured sound intensity at the new distance is 80 W/m².
Q7: What are some common sources of sound intensity and distance?
A7: Some common sources of sound intensity and distance include:
- Roaring engines: The sound intensity of a roaring engine decreases with distance from the source.
- Music: The sound intensity of music decreases with distance from the source.
- Noise pollution: The sound intensity of noise pollution decreases with distance from the source.
Q8: How can you measure sound intensity and distance?
A8: Sound intensity and distance can be measured using various instruments, including:
- Sound level meters: These instruments measure the sound intensity in decibels (dB).
- Distance measuring devices: These instruments measure the distance from the source.
Conclusion
In conclusion, the relationship between sound intensity and distance is inversely proportional, meaning that the sound intensity decreases with distance from the source. We have answered some frequently asked questions related to sound intensity and distance, and provided examples of how to calculate the new sound intensity at a given distance from the source.
References
- [1]: "Acoustics: An Introduction to Its Physical Principles and Applications" by Allan D. Pierce
- [2]: "The Physics of Sound" by Lawrence E. Kinsler
- [3]: "Sound and Vibration" by David G. Leventhall