The relationship between velocity, frequency, and wavelength is:

In this case we're given a scenario where  and . The velocities equal each other because the problem states it has a constant velocity. Therefore we can set these equations equal to each other:

Notice that the f's cancel out:

Divide both sides by two:

The relationship between frequency and wavelength determines the velocity:

The frequency is the inverse of the period. We can substitute this into the equation above.

In the question, both of the notes are played at the same time in the same location, so they both should have the same velocity. We can set the equation for each tone equal to each other.

We are told that . Substitute into our equation.

We can cancel the period from each side of the equation, leaving the relationship between the two wavelengths.

The wavelength of the first wave is equal to half the wavelength of the second. This means that the wavelength for the tone with a longer period will have a longer wavelength as well.

The relationship between frequency and period is .

Plug in our given value:

The wavelength of a wave is defined as the distance from a point on the wave to the same point on the wave (crest to crest or trough to trough). The distance between peaks is .

The amplitude of wave is defined as the distance the wave displaces from the equilibrium point.  In this case, the wave displaces  from the axis (the equilibrium point).

The speed of the wave along the Slinky depends on the mass of the Slinky itself and the tension caused by stretching it. Since both of these things have not changed, the wave speed remains constant.

The wave speed is equal to the wavelength multiplied by the frequency.

Since she is moving her hand faster, the frequency has increased. Since the velocity has not changed, an increase in the frequency would decrease the wavelength

The frequency at which standing waves are produced is known as the resonant frequencies. When two objects are brought near each other, and they both make standing waves at the same frequency, there is resonance in the system. For example, if you have two tuning forks of the same note, you can tap one and bring it close (but not touch) the other. Then if you silence the first tuning fork and listen, you will hear the second fork ringing as well because it vibrates at the same frequency.

This is an example of the doppler effect.  In this case the source is moving away from a stationary observer.  Therefore the corresponding equation is

When two waves are superimposed, the interference can be either constructive or destructive. In this case the interference is destructive, which means our resultant amplitude will be the difference of the two given amplitudes.

That means our new amplitude will be .

We can calculate the frequency of the beat using the equation

This is the beat frequency which means that the other string is off by   either higher or lower.