Textbook Question
A friend of yours is loudly singing a single note at 400 Hz while racing toward you at 25.0 m/s on a day when the speed of sound is 340 m/s. What frequency do you hear?
2
views
Ch 16: Traveling Waves
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796
Not the one you use?Change textbookSelect a different textbook
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 38a
What are the sound intensity levels for sound waves of intensity 3.0 x 10-6 W/m2?
Verified step by step guidance1
Step 1: Recall the formula for calculating the sound intensity level (in decibels, dB): \( L = 10 \cdot \log_{10} \left( \frac{I}{I_0} \right) \), where \( I \) is the intensity of the sound wave, and \( I_0 \) is the reference intensity, typically \( 1.0 \times 10^{-12} \; \text{W/m}^2 \).
Step 2: Substitute the given intensity \( I = 3.0 \times 10^{-6} \; \text{W/m}^2 \) and the reference intensity \( I_0 = 1.0 \times 10^{-12} \; \text{W/m}^2 \) into the formula: \( L = 10 \cdot \log_{10} \left( \frac{3.0 \times 10^{-6}}{1.0 \times 10^{-12}} \right) \).
Step 3: Simplify the fraction inside the logarithm: \( \frac{3.0 \times 10^{-6}}{1.0 \times 10^{-12}} = 3.0 \times 10^{6} \).
Step 4: Take the logarithm of \( 3.0 \times 10^{6} \): \( \log_{10}(3.0 \times 10^{6}) = \log_{10}(3.0) + \log_{10}(10^{6}) \). Use the property \( \log_{10}(10^{n}) = n \) to simplify \( \log_{10}(10^{6}) = 6 \).
Step 5: Combine the results: \( L = 10 \cdot (\log_{10}(3.0) + 6) \). Use a calculator or logarithmic table to find \( \log_{10}(3.0) \), then multiply by 10 to get the final sound intensity level in decibels.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
2mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Sound Intensity
Sound intensity is defined as the power per unit area carried by a sound wave. It is measured in watts per square meter (W/m²) and represents how much energy the sound wave transmits through a given area. Higher intensity levels correspond to louder sounds, while lower levels indicate quieter sounds.
Recommended video:
Guided course
04:25
Sound Intensity Level and the Decibel Scale
Decibel Scale
The decibel (dB) scale is a logarithmic scale used to measure sound intensity levels. It quantifies sound intensity relative to a reference intensity, typically 10⁻¹² W/m², using the formula L = 10 log₁₀(I/I₀), where L is the sound level in decibels, I is the intensity of the sound, and I₀ is the reference intensity. This scale allows for easier comparison of sound levels, as it compresses a wide range of intensities into a manageable numerical format.
Recommended video:
Guided course
04:25Sound Intensity Level and the Decibel Scale
Logarithmic Relationships
Logarithmic relationships are fundamental in physics, particularly in the context of sound intensity and the decibel scale. Since the human ear perceives sound intensity logarithmically, a small increase in decibel level corresponds to a significant increase in actual intensity. Understanding this relationship is crucial for interpreting sound levels and their effects on human perception.
Recommended video:
Guided course
03:43Relationships Between Force, Field, Energy, Potential
Related Practice
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?
2
views
Textbook Question
FIGURE P16.45 is a snapshot graph at t = 0 s of a 5.0 Hz wave traveling to the left. Write the displacement equation for this wave.
1
views
Textbook Question
A bat locates insects by emitting ultrasonic 'chirps' and then listening for echoes from the bugs. Suppose a bat chirp has a frequency of 25 kHz. How fast would the bat have to fly, and in what direction, for you to just barely be able to hear the chirp at 20 kHz?
2
views
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?
2
views
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?