Question

As the wavelength of a wave in a uniform medium increases, then what will happen with its speed?

Answer 1

1. Wavelength is the property of a wave that shows the distance between two successive identical points. They can either be the distance between two successive crests, troughs, or even the identical mean positions.
2. The given diagram marks the wavelength of a wave.

1. Speed of the Wave / Wave Speed can be defined as the distance that a wave travels in a given amount of time.
2. Wave Speed depends upon these four factors:

Medium

Temperature

Frequency

Wavelength

1. As the law of refraction shows, when a wave travels from a rarer to a denser medium, the speed of the wave decreases. And when it travels from denser to rarer, the speed of the wave increases.
2. In the case of uniformity, the speed of the wave is highest in dense materials (like solid) and slower in less dense materials (like water or gas)
3. As temperature affects the density of the medium and so the vibrations of the medium particles. Hence, the higher the temperature, the higher will be the speed of the wave.
4. As per the mathematical relation of the speed of the wave with its wavelength and frequency$Speedofthewave\left(\nu \right)=Wavelength\left(\lambda \right)\times Frequency\left(\upsilon \right)$
5. As the frequency of the wave increase, the wavelength will decrease.
6. Even though wave speed is calculated using the frequency and the wavelength, the wave speed does not depend upon these quantities.
7. So, the speed of a sound wave depends on the properties of the medium (like density) through which it moves and the only way to change the speed is by altering the properties of the medium.
8. Therefore, in a uniform medium, the increase in the wave's wavelength will not affect the wave speed as it will reduce the frequency of the wave accordingly.