As the wavelength of a wave in a uniform medium increases, its speed will ?
Same concept as for this question:
"Doubling the frequency of a wave source doubles the speed of the waves"
As the wavelength of a wave in a uniform medium increases, its speed will remain constant. The speed of a wave in a medium is determined by the properties of the medium itself and is not affected by the wavelength. Therefore, changing the wavelength of a wave does not change its speed in a uniform medium.
To determine how the speed of a wave changes as its wavelength increases in a uniform medium, we need to understand the relationship between wavelength and speed. This relationship is governed by a property of the medium called the "wave speed" or "phase velocity."
In a uniform medium, the wave speed is determined by the properties of the medium itself, such as its density and elasticity. For example, in a mechanical wave traveling through a stretched string, the wave speed depends on the tension in the string and the mass per unit length.
The general relationship between wavelength (λ), frequency (f), and wave speed (v) is given by the equation: v = f * λ. This equation is known as the wave equation.
Now, let's consider the scenario where the wavelength increases while the frequency remains constant. According to the wave equation, if the frequency is constant and the wavelength increases, the wave speed (v) must also increase.
This can be intuitively understood by imagining a wave traveling through a uniform medium. As the wavelength increases, the wave "stretches out," covering more distance in each complete cycle. Therefore, the wave must travel at a faster speed to maintain the same frequency.
In conclusion, as the wavelength of a wave in a uniform medium increases, its speed will also increase, assuming the frequency remains constant.