afraid / anxious
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afraid
To have a feeling of fear, fright, or great worry. Often used in the impersonal expression 'jemandem ist/wird bang' (someone is/becomes afraid).
Mir wurde plötzlich ganz bang, als ich das unheimliche Geräusch im Keller hörte.
I suddenly became very afraid when I heard the eerie noise in the basement.
anxious about
To worry intensely about the well-being or safety of someone or something.
Die Mutter war den ganzen Abend bang um ihre Tochter, die nicht nach Hause kam.
The mother was anxious about her daughter all evening because she did not come home.
In the expression 'jemandem ist/wird bang' (someone is/becomes afraid), the person who feels fear is in the dative. The construction is impersonal; the subject is not the person themself.
Mir wurde auf einmal ganz bang ums Herz.
All at once, my heart became very anxious.
When you worry about someone or something, you use the fixed structure 'bang sein um' (to be anxious about) followed by the accusative.
Ich bin bang um seine Gesundheit.
I am anxious about his health.
The word 'bang' (afraid/anxious) belongs more to elevated or written language. It sounds somewhat more formal or poetic.
Dem Seemann wurde bang, als der Sturm aufzog.
The sailor became afraid as the storm came up.
A common and active use is the expression 'jemandem bange machen' (to frighten someone / to make someone afraid). It means to scare someone or make them afraid.
Der große Hund hat dem kleinen Kind bange gemacht.
The big dog frightened the small child.
anxious / fearful
Both words describe fear or anxiety in a particular situation. „Bang“ is often used in the impersonal expression „jemandem ist bang“ and describes a momentary feeling, while „ängstlich“ tends to characterize the person or their behavior. „Bang“ often fits a current feeling, while „ängstlich“ describes an anxious nature.
Dem Kind ist vor dem starken Gewitter bang.
The child is frightened by the severe thunderstorm.
Das Kind ist wegen des starken Gewitters ängstlich.
The child is anxious because of the severe thunderstorm.
