The frequency \((f)\) of a wave is defined as the number of wavelengths per second which travel past a given point. a) For a wave traveling at a given speed, \(c\), how does the frequency depend on the wavelength, if at all? b) Provide a mathematical expression showing the relationship between \(f, \lambda\) and \(c\) for a wave. (Hint: consider how you determined answers to CTQ 2ab).

Short Answer

Expert verified
a) The frequency depends on the wavelength inversely, given the speed of the wave is constant. b) The mathematical relationship is given by \(f = \frac{c}{\lambda}\), where \(c\) is the wave speed, \(f\) is the frequency, and \(\lambda\) is the wavelength.

Step by step solution

01

Define the Terms

First, understand what the terms mean. The frequency (\(f\)) of a wave is the number of waves passing a point per second. A wavelength (\(\lambda\)) is the distance over which the wave's shape repeats. The speed (\(c\)) is the distance traveled by the wave per unit of time. In this case, we are told that the speed of the wave is constant.
02

Relate Frequency and Wavelength

Cause of wave speed being constant, if the wavelength increases, then fewer waves can pass a point per second. This implies that the frequency decreases. Similarly, if the wavelength decreases, more waves can pass a point per second, indicating an increase in frequency. Hence, frequency is inversely proportional to wavelength.
03

Formulate the Relationship Mathematically

The relationship derived in the previous step can be expressed mathematically as \(f = \frac{c}{\lambda}\). This equation shows how frequency (f), wavelength (\(\lambda\)) and speed (c) are related. The wave speed equals the product of its frequency and wavelength. This relationship holds true for all types of waves.

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