The question already mentions a possible answer, i.e. storing the signal and playing back at double the speed. That works, but is not practical for an application like time division multiplexing. At least not with the cassette tape style hardware which I was thinking of when I asked the question. Since then I learned that fast switching hardware for 'stretching' (in a sense) signals on to magnetic tape has already existed for a long time, in the form of video tape recorders.

A video signal has a much higher bandwidth than audio signals, and the maximum frequency magnetic tape can record for a given tape speed is limited. In order to record video signals on magnetic tape with a linear write head in the same style as for audio tape, you would need a much higher tape speed and a much longer tape, which would be impractical. Instead, VCR builders used helical scan. In helical scan, a pair of read/write heads sits on the sides of a drum that rotates rapidly. The magnetic tape is guided around half of the drum in a diagonal fashion, so that the read heads read diagonal slices of tape. In this way a number of diagonal tracks can sit on the tape side by side.

A similar trick could be used for this question. Instead of a helical scan, you can have a drum with read/write heads that just write sections of tape linearly. To do a two way TDM you could have a drum with four write heads, with an opposing pair of heads dedicated to each of a pair of input channels. Instead of the drum moving much faster than the tape, we can have the write heads move at half of the tape speed, with the tape wrapped around 180° of the drum. In this way each write head writes a section of tape, with two heads writing their own section at the same time. The result is a tape that contains intervals of signals from both input channels, squeezed to take up half of their original time and doubling the frequency, with intervals of both input channels alternating.

A second fixed read head can then read the tape with the alternating intervals, resulting in a TDM signal with data from each original signal alternating.

To demultiplex, a reverse setup can be used.

But for audio signals multiplexing on to a high bandwidth electrical signal, Dave Tweeds answer is much more practical.

The question already mentions a possible answer, i.e. storing the signal and playing back at double the speed. That works, but is not practical for an application like time division multiplexing. At least not with the cassette tape style hardware which I was thinking of when I asked the question. Since then I learned that fast switching hardware for 'stretching' (in a sense) signals on to magnetic tape has already existed for a long time, in the form of video tape recorders.

A video signal has a much higher bandwidth than audio signals, and the maximum frequency magnetic tape can record for a given tape speed is limited. In order to record video signals on magnetic tape with a linear write head in the same style as for audio tape, you would need a much higher tape speed and a much longer tape, which would be impractical. Instead, VCR builders used helical scan. In helical scan, a pair of read/write heads sits on the sides of a drum that rotates rapidly. The magnetic tape is guided around half of the drum in a diagonal fashion, so that the read heads read diagonal slices of tape. In this way a number of diagonal tracks can sit on the tape side by side.

A similar trick could be used for this question. Instead of a helical scan, you can have a drum with read/write heads that just write sections of tape linearly. To do a two way TDM you could have a drum with four write heads, with an opposing pair of heads dedicated to each of a pair of input channels. Instead of the drum moving much faster than the tape, we can have the write heads move at half of the tape speed, with the tape wrapped around 180° of the drum. In this way each write head writes a section of tape, with two heads writing their own section at the same time. The result is a tape that contains intervals of signals from both input channels, squeezed to take up half of their original time and doubling the frequency, with intervals of both input channels alternating.

A second fixed read head can then read the tape with the alternating intervals, resulting in a TDM signal with data from each original signal alternating. You only need a short loop of magnetic tape that loops between the write head drum and the fixed read head and back again. Although wear on that loop of tape might become a problem.

To demultiplex, a reverse setup can be used.

But for audio signals multiplexing on to a high bandwidth electrical signal, Dave Tweeds answer is much more practical.