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
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 42a
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?
Verified step by step guidance1
Identify the problem as a Doppler Effect scenario, where the frequency of a sound changes due to the relative motion between the source (your friend) and the observer (you). The formula for the observed frequency \( f' \) is: \( f' = f \frac{v + v_o}{v - v_s} \), where \( f \) is the source frequency, \( v \) is the speed of sound, \( v_o \) is the speed of the observer, and \( v_s \) is the speed of the source.
Since you (the observer) are stationary, \( v_o = 0 \). The formula simplifies to: \( f' = f \frac{v}{v - v_s} \).
Substitute the given values into the formula: \( f = 400 \ \text{Hz} \), \( v = 340 \ \text{m/s} \), and \( v_s = 25.0 \ \text{m/s} \). The equation becomes: \( f' = 400 \cdot \frac{340}{340 - 25.0} \).
Simplify the denominator: \( 340 - 25.0 = 315.0 \). The equation now reads: \( f' = 400 \cdot \frac{340}{315.0} \).
To find the observed frequency \( f' \), calculate the fraction \( \frac{340}{315.0} \) and multiply it by 400. This will give you the frequency you hear as your friend approaches.
Verified video answer for a similar problem:
This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4mWas this helpful?
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Doppler Effect
The Doppler Effect describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the wave. When the source of sound moves toward an observer, the frequency increases, resulting in a higher pitch. Conversely, if the source moves away, the frequency decreases. This phenomenon is crucial for understanding how the frequency of sound changes based on the relative motion of the source and the observer.
Recommended video:
Guided course
07:40
The Doppler Effect
Frequency and Wavelength
Frequency is the number of cycles of a wave that occur in a unit of time, typically measured in Hertz (Hz). Wavelength is the distance between successive crests of a wave. The relationship between frequency and wavelength is inversely proportional; as frequency increases, wavelength decreases. Understanding this relationship is essential for calculating the perceived frequency of sound when the source is in motion.
Recommended video:
Guided course
05:08Circumference, Period, and Frequency in UCM
Speed of Sound
The speed of sound is the rate at which sound waves propagate through a medium, which varies depending on factors like temperature and the medium itself. In air at room temperature, the speed of sound is approximately 340 m/s. This speed is critical for calculating the observed frequency of sound when the source is moving, as it influences how quickly the sound waves reach the observer.
Recommended video:
Guided course
05:17Standing Sound Waves
Related Practice
Textbook Question
What are the sound intensity levels for sound waves of intensity 3.0 x 10-6 W/m2?
1
views
Textbook Question
String 1 in FIGURE P16.47 has linear density 2.0 g/m and string 2 has linear density. A student sends pulses in both directions by quickly pulling up on the knot, then releasing it. What should the string lengths L₁ and L₂ be if the pulses are to reach the ends of the strings simultaneously?
1
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