Final answer:
To change the wavelength while keeping frequency the same, one should change the medium in which a wave is traveling. The frequency of a wave depends on the source, but the speed and wavelength can change when the wave enters a medium with a different density or refractive index.
Step-by-step explanation:
To produce a different value of wavelength while maintaining the same frequency, you would need to change the medium through which the wave is traveling. For example, when light travels from air into water, its speed decreases due to the higher refractive index of water, yet the frequency remains unchanged because frequency is dependent on the source of the light. Given the relationship V = fλ, where V is the speed of the wave, f is the frequency, and λ is the wavelength, a change in speed (V) caused by a change in medium will result in a change in wavelength (λ) if the frequency (f) remains constant.
Conversely, changes in amplitude or temperature do not directly lead to changes in wavelength while keeping frequency constant. The speed of sound does depend on the properties of the medium, which can be affected by temperature, but temperature itself does not change the wavelength independently of medium. Therefore, among the provided options, changing the medium is the correct method to alter wavelength while keeping frequency the same.