For a Given Wave: If the Frequency Doubles, the Wavelength Explained
Introduction:
Waves are a fundamental concept in physics and have various properties that we can study. One important characteristic of a wave is its frequency, which refers to the number of complete cycles or oscillations it undergoes in a given time. Another crucial property is wavelength, which describes the distance between any two corresponding points on the wave, such as two consecutive crests or troughs. In this article, we will explore what happens to the wavelength of a wave when its frequency doubles.
I. Understanding Frequency and Wavelength:
To comprehend the relationship between frequency and wavelength, let’s first clarify their definitions. Frequency is typically measured in hertz (Hz) and represents the number of complete cycles the wave completes in one second. On the other hand, wavelength is often measured in meters (m) and represents the distance between any two corresponding points on the wave.
II. The Relationship between Frequency and Wavelength:
According to the wave equation, the speed of a wave (v) is equal to the product of its frequency (f) and wavelength (λ). Mathematically, this relationship can be represented as v = f * λ.
III. Doubling the Frequency:
Now, let’s examine what happens to the wavelength when the frequency of a wave doubles. Suppose we have an initial wave with a specific frequency and wavelength. When we double the frequency, the equation becomes 2f * λ = v, where \”2f\” represents the new frequency.
IV. The Implication for Wavelength:
To determine the new wavelength, we rearrange the equation to isolate λ. Dividing both sides of the equation by 2f gives us:
λ = v / 2f.
Therefore, if the frequency of a wave doubles, the wavelength becomes half of its original value.
V. Example Calculation:
To illustrate this relationship, let’s consider an example. Suppose we have a wave with a frequency of 100 Hz and a corresponding wavelength of 2 meters. If we double the frequency to 200 Hz, the new wavelength would be:
λ = v / 2f
= 2 m / (2 * 200 Hz)
= 2 m / 400 Hz
= 0.005 meters or 5 millimeters.
Conclusion:
In summary, when the frequency of a wave doubles, the wavelength is halved. This relationship is demonstrated by the wave equation, where the speed of a wave is equal to the product of its frequency and wavelength. By understanding this relationship, we can analyze the behavior of waves and predict how changes in frequency will affect their corresponding wavelengths.
