Question

how could you increase the frequency and decrease the wavelength of a wave in a marshmallow wave machine? Does changing the frequency and wavelength change the speed of the wave?

Answer 1

Short answer
- To increase the frequency: drive the wave faster — move your hand (or the driving end) back-and‑forth more rapidly.
- To decrease the wavelength: either increase the driving frequency (for a fixed medium) or reduce the wave speed of the marshmallow chain (loosen the string / reduce tension, or increase the mass per unit length).
- Does that change the wave speed? Usually no: for a given medium the wave speed is set by the medium (tension and mass distribution) and does not change just because you drive it at a different frequency. Frequency and wavelength adjust so that v = f·λ.

Why (brief)
- For transverse waves on a string-like machine the speed v ≈ sqrt(T/μ) (T = tension, μ = mass per unit length). For a mass-on-springs chain the speed depends on spring stiffness and mass of the pieces. Those medium properties set v.
- The measured relationship v = fλ means if v stays the same and you raise f, λ must fall. If you want to make λ shorter without changing f, you must lower v (for example by loosening the string or adding mass).

Practical notes
- Increasing your hand frequency is the easiest way to get shorter wavelengths up to the limits of your motion and the device.
- Loosening the connection, making marshmallows heavier, or using softer connectors will lower v and shorten λ for a given f.
- At very high frequencies or large amplitudes you may see dispersion or nonlinear effects so v can depend on frequency; in ordinary classroom marshmallow wave machines that rarely matters.