How do frequency and wavelength change with wave speed?

Wave speed is directly proportional to frequency and inversely proportional to wavelength.

In more detail, the speed of a wave is determined by its frequency and wavelength. These three properties are interconnected through the wave equation, v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength. This equation shows that the speed of a wave is equal to the product of its frequency and wavelength.

If the speed of a wave increases while the frequency remains constant, the wavelength must also increase. This is because the wave has to cover more distance in the same amount of time. Conversely, if the speed decreases while the frequency remains constant, the wavelength must decrease. This is because the wave covers less distance in the same amount of time.

Similarly, if the speed of a wave increases while the wavelength remains constant, the frequency must also increase. This is because the wave has to complete more cycles in the same amount of time. Conversely, if the speed decreases while the wavelength remains constant, the frequency must decrease. This is because the wave completes fewer cycles in the same amount of time.

However, it's important to note that in many physical systems, the speed of a wave is determined by the medium through which it travels and can't be easily changed. For example, the speed of light is constant in a vacuum, and the speed of sound is determined by the properties of the air or other medium. In these cases, changing the frequency of the wave will result in a corresponding change in the wavelength, and vice versa, to ensure that the wave equation still holds true.

IB Physics Tutor Summary: In summary, wave speed is related to both frequency and wavelength. If wave speed changes, frequency and wavelength adjust to maintain balance. Think of it as a balancing act: when one goes up, the other must adjust accordingly to keep the wave moving correctly. Remember, the medium affects wave speed, which in turn influences frequency and wavelength relationships.