Table of contents

0. Math Review31m
- Math Review
  31m
1. Intro to Physics Units1h 29m
2. 1D Motion / Kinematics3h 56m
3. Vectors2h 43m
4. 2D Kinematics1h 42m
5. Projectile Motion3h 6m
6. Intro to Forces (Dynamics)3h 22m
7. Friction, Inclines, Systems2h 44m
8. Centripetal Forces & Gravitation7h 26m
9. Work & Energy1h 59m
10. Conservation of Energy2h 54m
11. Momentum & Impulse3h 40m
12. Rotational Kinematics2h 59m
13. Rotational Inertia & Energy7h 4m
14. Torque & Rotational Dynamics2h 5m
15. Rotational Equilibrium3h 39m
16. Angular Momentum3h 6m
17. Periodic Motion2h 9m
18. Waves & Sound3h 40m
19. Fluid Mechanics4h 27m
20. Heat and Temperature3h 7m
21. Kinetic Theory of Ideal Gases1h 50m
22. The First Law of Thermodynamics1h 26m
23. The Second Law of Thermodynamics3h 11m
24. Electric Force & Field; Gauss' Law3h 42m
25. Electric Potential1h 51m
26. Capacitors & Dielectrics2h 2m
27. Resistors & DC Circuits3h 8m
28. Magnetic Fields and Forces2h 23m
29. Sources of Magnetic Field2h 30m
30. Induction and Inductance3h 38m
31. Alternating Current2h 37m
32. Electromagnetic Waves2h 14m
33. Geometric Optics2h 57m
34. Wave Optics1h 15m
35. Special Relativity2h 10m

18. Waves & Sound

Velocity of Transverse Waves

Physics

18. Waves & Sound

Velocity of Transverse Waves

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Problem 17a

Textbook Question

What is the frequency of an electromagnetic wave that has the same wavelength as a 2.5 kHz sound wave in water?

Verified step by step guidance

Step 1: Understand the problem. The goal is to find the frequency of an electromagnetic wave that has the same wavelength as a sound wave in water. The relationship between wavelength, frequency, and speed is given by the formula:

v = f λ

, where

v

is the speed,

f

is the frequency, and

λ

is the wavelength.

Step 2: Calculate the wavelength of the sound wave in water. Use the formula

λ = v / f

, where the speed of sound in water is approximately 1500 m/s and the frequency of the sound wave is 2.5 kHz (or 2500 Hz). Substitute these values into the formula to find the wavelength.

Step 3: Recognize that the electromagnetic wave has the same wavelength as the sound wave. The speed of electromagnetic waves in a vacuum (and approximately in air) is the speed of light,

c = 3.0 × 10

⁸ m/s. Use the formula

f = c / λ

to calculate the frequency of the electromagnetic wave.

Step 4: Substitute the wavelength calculated in Step 2 into the formula for the electromagnetic wave frequency. Use

f = c / λ

, where

c

is the speed of light and

λ

is the wavelength.

Step 5: Simplify the expression to find the frequency of the electromagnetic wave. Ensure units are consistent throughout the calculation (e.g., meters for wavelength and seconds for time). The result will give the frequency of the electromagnetic wave in Hz.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. They travel at the speed of light in a vacuum and encompass a wide range of frequencies and wavelengths, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. The relationship between frequency and wavelength is fundamental to understanding their behavior.

Wave Equation

The wave equation relates the speed of a wave to its frequency and wavelength, expressed as v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. This equation is crucial for calculating the frequency of an electromagnetic wave when its wavelength is known. For electromagnetic waves in a vacuum, the speed is approximately 3 x 10^8 m/s.

Sound Waves in Water

Sound waves are mechanical waves that require a medium to travel, such as air, water, or solids. In water, sound travels faster than in air due to the higher density and elasticity of the medium. The frequency of a sound wave, such as the 2.5 kHz mentioned, is related to its wavelength and speed in water, which is essential for comparing it to the frequency of an electromagnetic wave with the same wavelength.

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Textbook Question

A 10.0-m-long wire of mass 138 g is stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first meet?

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Textbook Question

A uniform cable 2.0-m long hangs vertically under its own weight. Determine the speed of waves on the cable as a function the distance y (positive down from the top of the cable, where y = 0).

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Textbook Question

When a guitar string plays the note 'A,' the string vibrates at 440 Hz. What is the period of the vibration?

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Textbook Question

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Multiple Choice

A 2 m long string is arranged as shown in the figure below. If the mass of the string is 0.5 kg, what would the frequency be of a wave with a 2 cm wavelength?

A rope with length 2.50 m and mass 0.10 kg is stretched and pulled to create transverse waves of frequency 40.0 Hz and wavelength of 0.750 m. How much tension is exerted on the rope?

An oscillating blade creates waves on a string. If the amplitude of the wave doubles, what happens to the wavelength λ and v?

The string in FIGURE P16.59 has linear density μ. Find an expression in terms of M, μ, and θ for the speed of waves on the string.

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