Record a tape cassette

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I have a tape cassette that I need to convert to a digital format mp3 or wav.
The problem I am having is that all my good tape decks have died a long time ago and I couldn't find a decent tape deck with line out when I searched few years ago.
The only thing I have now is an old Sony radio that has a tape deck but no line out, only a headphones socket.
I tried to record the tape using Audacity and had a Snowball microphone in front of of one of the speakers. The recording wasn't bad but didn't sound as good as when I listen to the tape.
So I tried to record by connecting an audio cable to the headphones socket and the other end to line in on my PC. The recorded sound was not as good as using a microphone.
Is there anything else I can try to get a better recording? Should I use a different recording software instead of Audacity?
I am still looking for a tape deck which has a line out, in case anyone knows where to buy them these days.
Thanks for all suggestions.

[Bwaak]

Headphone output should not be that bad provided the volume is not too low to cause hiss and not too high to cause distortion. You may need to adjust attenuation on your computer.

I cannot believe that recording off a mic sounds better than off a headphone output.

[pandy]

Level can be too high - also headphone output may not work correctly with high impedance load - you could create simple, resistor based attenuator and dummy load to improve audio quality.

[johns0]

Just go to a thrifty shop and buy a tape deck.

[Subtitles]

Headphone output should not be that bad provided the volume is not too low to cause hiss and not too high to cause distortion. You may need to adjust attenuation on your computer.

I cannot believe that recording off a mic sounds better than off a headphone output.

This Sony radio is quite old and the headphones output aren't that great.
I found another portable radio by Panasonic that has a tape deck and the headphones jack sounds much better. So all is good now.

Is there a way to listen to the tape while recording is in progress using Audacity? When I insert the audio plug, there is no sound coming out of radio speakers obviously and the line out is muted during recording.

[netmask56]

https://www.frequencycast.co.uk/plusdeck.html

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https://www.frequencycast.co.uk/plusdeck.html

Thank you for the suggestion. It is a good solution.
This product has been discontinued as far as I can see.