Is temporal wavelength of a wave always equivalent to its spatial wavelength?

Question

I can't see how it would be possible for these two to be different.

Answer 1

For spatial, it is the number of occurrences per unit-distance.

For temporal it is per unit-time.

Yes they can be different.

Please see here:

Significance of wave number?

Both frequencies and consequently the phase (01) are expressed as angles in radian units. A full cycle is a $2\pi $ radians angle. That's why this factor in $\omega=2\pi / T$ and $k=2\pi / \lambda$. \begin{align} T \equiv & \text{time length for a full cycle of the phase at given space point = period} \tag{03a}\\ &\phi(x,t+T) =\phi(x,t)+2\pi \tag{03b}\\ \lambda \equiv & \text{space length for a full cycle of the phase at given time moment = wavelegth} \tag{04a}\\ & \phi(x+\lambda,t) =\phi(x,t)-2\pi \tag{04b} \end{align}

Answer 2

I don't think that the term "temporal wavelength" is used in physics. It is the first time that I see it. Wavelength is defined for a spatially periodic wave pattern corresponding to a periodic signal in time at a given location. The time interval corresponding to a spatial wavelength of a periodic wave is usually called period $T$ and is related to the frequency $f$ and wavelength $\lambda$ by $$T=\frac {1}{f}=\frac {\lambda}{v}$$ where $v$ is the wave velocity.

Thus there is always a correspondence between the spatial wavelength $\lambda$ and the time period $T$ of a periodic wave.