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Difficulty: MediumWaves, Sound, and Light

A communications antenna emits radio waves that travel through uniform atmospheric air. If the transmitter is adjusted to emit radio waves at a higher frequency, how do the speed and wavelength of the transmitted waves change?

  1. A
    The speed increases, and the wavelength remains unchanged.
  2. B
    The speed increases, and the wavelength increases.
  3. The speed remains constant, and the wavelength decreases.Answer
  4. D
    The speed remains constant, and the wavelength increases.

Answer

The speed remains constant, and the wavelength decreases.
In a uniform medium such as air, the speed of an electromagnetic wave is constant. According to the wave equation v=fλv = f \lambda, when the speed vv is constant, frequency ff and wavelength λ\lambda are inversely proportional. Therefore, increasing the frequency causes the wavelength to decrease while the speed remains unchanged.

Step-by-Step Solution

1
Identify the factor that determines wave propagation speed.
The speed of electromagnetic radio waves is constant in a uniform medium (v=cv = c in air).
Wave speed is an intrinsic property of the medium through which the wave travels, not the frequency of the source.
2
Apply the wave equation relating speed, frequency, and wavelength.
v=fλv = f \lambda, which rearranges to λ=vf\lambda = \frac{v}{f}.
This relationship mathematically couples frequency and wavelength for a given constant speed.
3
Determine the effect of increasing frequency on wavelength.
As frequency (ff) increases while speed (vv) remains fixed, wavelength (λ\lambda) must decrease proportionally.
Frequency and wavelength are inversely proportional when wave speed is held constant.

Key Concept

The speed of a wave is determined by the transmission medium, creating an inverse relationship between frequency and wavelength (v=fλv = f \lambda).
Estimated Time:1m 0s
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Topics

Waves, Sound, and Light

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