wavelength
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to be on the same wavelength
In a figurative sense, the way people harmonize with and understand each other.
Wir haben sofort gemerkt, dass wir auf der gleichen Wellenlänge sind.
We noticed right away that we were on the same wavelength.
wavelength
In physics, the distance between two consecutive points with the same phase of a wave, for example in light or sound.
Radiosender senden auf unterschiedlichen Wellenlängen.
Radio stations broadcast on different wavelengths.
The word is made up of 'die Welle' (the wave) and 'die Länge' (the length). So the physical meaning is quite literally 'the length of a wave.'
Die Wellenlänge von sichtbarem Licht ist extrem kurz.
The wavelength of visible light is extremely short.
The figurative meaning is used almost exclusively in the fixed expression 'auf der gleichen Wellenlänge sein/liegen' (to be on the same wavelength). The preposition 'auf' with the dative is fixed here.
Mein neuer Kollege und ich sind zum Glück auf der gleichen Wellenlänge.
Luckily, my new colleague and I are on the same wavelength.
You can recognize the physical meaning from a technical or scientific context, such as radio, physics, or light. You can almost always recognize the figurative, personal meaning from the fixed expression 'auf der gleichen/einer Wellenlänge sein' (to be on the same wavelength).
Der Sender hat seine Wellenlänge geändert.
The station changed its wavelength.
frequency
When two people get along well, German normally says that they are auf derselben Wellenlänge (on the same wavelength). Auf derselben Frequenz is also occasionally used figuratively, but sounds less usual in German. For a natural everyday expression, Wellenlänge is therefore usually the better choice.
Mara merkt sofort, dass sie und ihre neue Kollegin auf derselben Wellenlänge sind.
Mara immediately realizes that she and her new colleague are on the same wavelength.
Der Musiker sagt scherzhaft, dass er und seine neue Kollegin auf derselben Frequenz sind.
The musician jokingly says that he and his new colleague are on the same frequency.
