Let's say that I create a time varying magnetic field.
This field then cuts a conducting circular loop normally. The loop has two protruding wires. Will the protruding wires emit EM waves? I figured that the changing magnetic field will induce an emf in the loop and hence, current. However, will the wires emit EM waves? If so, will the EM waves have a specific emission frequency?
Will the protruding wires emit EM waves?
They don't have to. An example where they do not not would be for a spatially uniform magnetic field that increases linearly in time with a wire loop of fixed resistance, and a steady current in the loop and no current in the protruding wires. In this case the current in the wires is steady, and no radiation or waves are produced by the wires.
I figured that the changing magnetic field will induce an emf in the loop and hence, current.
Be very very careful about attributing causality. Instructors and textbooks that want to oversimplify might want to tell you that a changing magnetic field causes an electric field. But there is no basis for that. Electric fields and changing magnetic fields are related, and have values that are related. But correlation does not imply causation. You could just as easily say that circulating electric fields cause magnetic fields to change. Or that both things have a common cause. In fact, it's much more reasonable to say either one of those things.
Otherwise someone will claim that changing electric fields cause magnetic fields. You have to first have a thing to have it change. Once you have charge and current and electric fields and magnetic fields they can cause the fields to change. For instance
$$\frac{\partial \vec B}{\partial t}=-\vec\nabla \times \vec E$$ can tell you how the change of the magnetic field here and now is caused by the spatial variation of the electric field now.
And $$\frac{\partial \vec E}{\partial t}=\frac{1}{\epsilon_0}\left(-\vec J+\frac{1}{\mu_0}\vec\nabla \times \vec B \right)$$ can tell you how the change of the electric field here and now is caused by the current here and now and the spatial variation of the magnetic field now.
Or, an alternative could be to say the electric and magnetic field at any place or moment have a common cause (charge and current for instance). An example solution to Maxwell can be provided if both the electric and magnetic fields are each computed as the electric and magnetic parts of the electromagnetic field given by Jefimenko's equations:
$$\vec E(\vec r,t)=\frac{1}{4\pi\epsilon_0}\int\left[\frac{\rho(\vec r',t_r)}{|\vec r -\vec r'|}+\frac{\partial \rho(\vec r',t_r)}{c\partial t}\right]\frac{\vec r -\vec r'}{|\vec r -\vec r'|^2}\; \mathrm{d}^3\vec{r}' -\frac{1}{4\pi\epsilon_0c^2}\int\frac{1}{|\vec r-\vec r'|}\frac{\partial \vec J(\vec r',t_r)}{\partial t}\mathbb{d}^3\vec r'$$ and $$\vec B(\vec r,t)=\frac{\mu_0}{4\pi}\int\left[\frac{\vec J(\vec r',t_r)}{|\vec r -\vec r'|^3}+\frac{1}{|\vec r -\vec r'|^2}\frac{\partial \vec J(\vec r',t_r)}{c\partial t}\right]\times(\vec r -\vec r')\mathbb{d}^3\vec r'$$ where $t_r$ is actually a function of $\vec r'$, specifically $t_r=t-\frac{|\vec r-\vec r'|}{c}.$
These reduce to Coulomb and Biot-Savart only when those time derivatives are exactly zero, which is statics. So Jefimenko is an example of proper time dependent laws for the electromagnetic field. Note that both the electric and the magnetic part of the electromagnetic field have parts that depend on the time variation of current. And this is the term responsible for radiation and waves.
So you could use Jefimenko to show how both fields here and now are determined by charge and current (and their time variations) in the past.
However, will the wires emit EM waves?
The example I gave of a steady current in the wire loop and a linearly changing magnetic field has no radiation produced by the wire. And it meets your specification.
So, there is a current in the open loop and from that you may be very tempted to say that there is necessarily an alternating voltage, which would give you AC currents into the protruding wires. However these last two ideas are not correct.
You may choose any of several ways to see this. The simplest is to divide the current up into little segments of the loop and ask yourself what it has to be. The current due to the "EMF" created must cause a corresponding resistive loss, otherwise the EMF would move more charge until it did. This resistive loss makes it so that the voltage stays 0 along the whole loop. Another way to see this is to imagine connecting a voltmeter across the loop; if the EMF is $\mathcal E$ then will it measure $+\mathcal E/2$ going the "right" way along the loop to the opposite side or $-\mathcal E/2$ by going the "wrong" way along the loop to the opposite side?
Another way is to understand voltage as "generalized" voltage, which is not simply the line integral of the electric field but the electric field plus the time rate of change of the vector potential for the magnetic field. During electromagnetic induction these two effects necessarily cancel out locally.
