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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 proportional to both the frequency and the wavelength. If frequency or wavelength is doubled, the speed of the wave is also doubled, assuming the other parameter remains constant.

Step by step solution

01

Understanding the relationship between speed, frequency and wavelength

The equation c = 位f implies that the speed of an electromagnetic wave c is the product of the wave's wavelength 位 and its frequency f. This equation describes a simple linear relationship between these three quantities.
02

Determine how the speed varies with frequency

If we rearrange the equation to solve for speed, we will have \(c=f\lambda\). If the wavelength \(\lambda\) remains constant, then the speed \(c\) varies directly with the frequency \(f\). In other words, if we double the frequency of the wave, the wave's speed will also double.
03

Determine how the speed varies with wavelength

Again, if we look at the equation \(c=\lambda f\), this time keeping the frequency \(f\) constant, then the speed \(c\) varies directly with the wavelength \(\lambda\). This means that if we double the wavelength of the wave, the wave's speed will also double. That's because the speed of electromagnetic waves is directly proportional to both the frequency and the wavelength.

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