Textbook Question
A concert loudspeaker suspended high above the ground emits 35 W of sound power. A small microphone with a 1.0 cm² area is 50 m from the speaker. What is the sound intensity at the position of the microphone?
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Ch 16: Traveling Waves
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
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Table of contents
- Ch 01: Concepts of Motion35
- Ch 02: Kinematics in One Dimension75
- Ch 03: Vectors and Coordinate Systems58
- Ch 04: Kinematics in Two Dimensions60
- Ch 05: Force and Motion23
- Ch 06: Dynamics I: Motion Along a Line53
- Ch 07: Newton's Third Law27
- Ch 08: Dynamics II: Motion in a Plane52
- Ch 09: Work and Kinetic Energy56
- Ch 10: Interactions and Potential Energy50
- Ch 11: Impulse and Momentum56
- Ch 12: Rotation of a Rigid Body71
- Ch 13: Newton's Theory of Gravity52
- Ch 14: Fluids and Elasticity44
- Ch 15: Oscillations55
- Ch 16: Traveling Waves37
- Ch 17: Superposition39
- Ch 18: A Macroscopic Description of Matter53
- Ch 19: Work, Heat, and the First Law of Thermodynamics60
- Ch 20: The Micro/Macro Connection53
- Ch 21: Heat Engines and Refrigerators34
- Ch 22: Electric Charges and Forces40
- Ch 23: The Electric Field39
- Ch 24: Gauss' Law32
- Ch 25: The Electric Potential63
- Ch 26: Potential and Field57
- Ch 27: Current and Resistance42
- Ch 28: Fundamentals of Circuits39
- Ch 29: The Magnetic Field47
- Ch 30: Electromagnetic Induction60
- Ch 31: Electromagnetic Fields and Waves32
- Ch 32: AC Circuits63
- Ch 33: Wave Optics32
- Ch 34: Ray Optics57
- Ch 35: Optical Instruments30
- Ch 36: Special Relativity38
- Ch 37: The Foundations of Modern Physics25
- Ch 38: Quantization49
- Ch 39: Wave Functions and Uncertainty31
- Ch 40: One-Dimensional Quantum Mechanics35
- Ch 41: Atomic Physics18
- Ch 42: Nuclear Physics27
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook
Chapter 16, Problem 33
The intensity of electromagnetic waves from the sun is 1.4 kW/m² just above the earth's atmosphere. Eighty percent of this reaches the surface at noon on a clear summer day. Suppose you think of your back as a 30 cm x 50 cm rectangle. How many joules of solar energy fall on your back as you work on your tan for 1.0 h?
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Step 1: Calculate the area of your back. The dimensions are given as 30 cm x 50 cm. Convert these to meters (since the intensity is in kW/m²) and calculate the area using the formula: \( A = \text{length} \times \text{width} \).
Step 2: Determine the intensity of sunlight that reaches the surface. Since 80% of the sun's intensity reaches the surface, multiply the given intensity above the atmosphere (1.4 kW/m²) by 0.8 to find the effective intensity at the surface.
Step 3: Calculate the power incident on your back. Use the formula \( P = I \times A \), where \( I \) is the intensity at the surface (from Step 2) and \( A \) is the area of your back (from Step 1).
Step 4: Determine the total energy received over 1.0 hour. Use the formula \( E = P \times t \), where \( P \) is the power (from Step 3) and \( t \) is the time in seconds (convert 1.0 hour to seconds by multiplying by 3600).
Step 5: The result from Step 4 gives the total energy in joules that falls on your back during the 1.0-hour period. Ensure all units are consistent throughout the calculations.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Intensity of Electromagnetic Waves
The intensity of electromagnetic waves, measured in watts per square meter (W/m²), represents the power per unit area carried by the waves. In this context, the intensity of solar radiation from the sun is given as 1.4 kW/m², indicating how much solar energy is available per square meter just above the Earth's atmosphere.
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02:32
Wave Intensity
Energy Calculation
Energy can be calculated using the formula: Energy = Power × Time. In this scenario, the power reaching the surface of the Earth is 80% of the initial intensity, and the time is given as 1 hour. This calculation will help determine the total energy received by a specific area over a set duration.
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Area of Exposure
The area of exposure is crucial for determining how much energy falls on a surface. In this case, the back is modeled as a rectangle with dimensions 30 cm by 50 cm. Converting these dimensions to meters allows for accurate calculations of the energy received based on the intensity of solar radiation and the area exposed.
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Related Practice
Textbook Question
What are the sound intensity levels for sound waves of intensity 3.0 x 10-6 W/m2?
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Textbook Question
A loudspeaker at the origin emits a 120 Hz tone on a day when the speed of sound is 340 m/s. The phase difference between two points on the x-axis is 5.5 rad. What is the distance between these two points?
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Textbook Question
A sound wave with intensity 2.0 x 10-3 W/m2 is perceived to be modestly loud. Your eardrum is 6.0 mm in diameter. How much energy will be transferred to your eardrum while listening to this sound for 1.0 min?
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Textbook Question
A spherical wave with a wavelength of 2.0 m is emitted from the origin. At one instant of time, the phase at r = 4.0 m is π rad. At that instant, what is the phase at r = 3.5 m and at r = 4.5 m?
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Textbook Question
A sound source is located somewhere along the x-axis. Experiments show that the same wave front simultaneously reaches listeners at x = -7.0 m and x = ＋3.0 m. What is the x-coordinate of the source?
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