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 32
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?
Verified step by step guidance1
Determine the wavelength of the sound wave using the formula: , where is the speed of sound (340 m/s) and is the frequency (120 Hz).
Relate the phase difference to the distance between the two points using the formula: , where is the phase difference (5.5 rad), is the distance between the points, and is the wavelength.
Rearrange the formula to solve for : .
Substitute the known values for (5.5 rad) and (calculated in step 1) into the equation.
Simplify the expression to find the distance between the two points.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Wave Frequency
Frequency is the number of cycles of a wave that occur in a unit of time, typically measured in Hertz (Hz). In this context, the loudspeaker emits a tone at 120 Hz, meaning it produces 120 sound wave cycles per second. This frequency is crucial for determining the wavelength of the sound wave, which is essential for calculating the distance between points based on phase difference.
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Speed of Sound
The speed of sound is the rate at which sound waves propagate through a medium, which in this case is air. Given as 340 m/s, this value is used to relate frequency and wavelength through the equation v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength. Understanding this relationship is key to solving for the distance between points based on their phase difference.
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Phase Difference
Phase difference refers to the difference in the phase of two waves at a given point in time, measured in radians. A phase difference of 5.5 radians indicates how far one wave is ahead or behind another. This concept is critical for determining the distance between two points on the x-axis, as the distance can be calculated using the formula Δx = (φ/2π)λ, where φ is the phase difference and λ is the wavelength.
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Related Practice
Textbook Question
What is the speed of sound in air (a) on a cold winter day in Minnesota when the temperature is -25°F, and (b) on a hot summer day in Death Valley when the temperature is 125°F?
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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
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?
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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