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Chapter 29: Problem 5

The speed of an electromagnetic wave is given by \(c=\lambda f .\) How does the speed depend on frequency? On wavelength?

Short Answer

Expert verified
The speed of an electromagnetic wave is directly dependent on both its frequency and wavelength. If one increases while the other stays constant, the speed must also increase, and vice versa.

Step by step solution

01

Understand The Equation

The equation provided is an equation of direct proportionality. The multiplication between wavelength and frequency gives the speed of light. This shows that the speed of an electromagnetic wave is directly proportional to both its frequency and its wavelength.
02

Determine Dependence On Frequency

Since the speed of light 'c' is a constant, we can rewrite the equation as \(f = \frac{c}{\lambda}\). Here, if the wavelength remains constant, the frequency must also remain constant to maintain the speed of light. Thus, the speed of an electromagnetic wave (light) is directly dependent on the frequency.
03

Determine Dependence On Wavelength

Similarly, we can rewrite the equation as \(\lambda = \frac{c}{f}\). If the frequency remains constant, the wavelength must also remain constant to maintain the speed of light. This shows that the speed of an electromagnetic wave is also directly dependent on the wavelength.

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Most popular questions from this chapter

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