Textbook Question
What is the frequency of an electromagnetic wave that has the same wavelength as a 2.5 kHz sound wave in water?
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 27
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?
Verified step by step guidance1
Step 1: Convert the given temperatures from Fahrenheit to Celsius using the formula: \( T_{C} = \frac{5}{9}(T_{F} - 32) \). For part (a), substitute \( T_{F} = -25 \) into the formula. For part (b), substitute \( T_{F} = 125 \) into the formula.
Step 2: Use the formula for the speed of sound in air: \( v = 331.4 + 0.6 \cdot T_{C} \), where \( T_{C} \) is the temperature in Celsius. Substitute the converted temperatures from Step 1 into this formula for both cases.
Step 3: Simplify the expression for \( v \) for each case by performing the arithmetic operations. This will give the speed of sound in air for the cold winter day and the hot summer day.
Step 4: Ensure the units of the final speed are in meters per second (m/s), as the formula \( v = 331.4 + 0.6 \cdot T_{C} \) inherently provides the speed in m/s.
Step 5: Interpret the results conceptually: The speed of sound increases with temperature because warmer air molecules move faster, facilitating quicker propagation of sound waves.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Speed of Sound
The speed of sound is the distance that sound waves travel through a medium in a given amount of time. In air, this speed is influenced by factors such as temperature, humidity, and pressure. Generally, sound travels faster in warmer air because the molecules are more energetic and can transmit the sound waves more quickly.
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Standing Sound Waves
Effect of Temperature on Sound Speed
Temperature significantly affects the speed of sound in air. As temperature increases, the speed of sound also increases due to the greater kinetic energy of air molecules, which facilitates faster propagation of sound waves. Conversely, at lower temperatures, the speed of sound decreases as molecular motion slows down.
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Conversion of Temperature Units
To accurately calculate the speed of sound based on temperature, it is often necessary to convert temperatures from Fahrenheit to Celsius or Kelvin. The formula for conversion from Fahrenheit to Celsius is C = (F - 32) × 5/9. Understanding this conversion is essential for applying the correct temperature values in the speed of sound formula.
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Related Practice
Textbook Question
A hammer taps on the end of a 4.00-m-long metal bar at room temperature. A microphone at the other end of the bar picks up two pulses of sound, one that travels through the metal and one that travels through the air. The pulses are separated in time by 9.00 ms. What is the speed of sound in this metal?
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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 15-cm-long aluminum tank is filled with ethyl alcohol. A high-frequency ultrasound wave travels horizontally through one wall of the tank and then through the alcohol. There are 275 times more cycles of the wave in the alcohol than in the aluminum wall. How thick is the wall of the tank?
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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