A palindrome for blowing a horn could be: 'toot'.
A palindrome for the sound of a horn is "toot."
"Tooting" your Own Horn meaning For many generations, here in the US the term, to "Toot [or blow] your own horn," means to brag, or do or say something to draw attention to ones self; "show off, act out, etc."
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Honk!
"Vroom" is a palindrome for the sound of a horn.
No, there is not a palindrome for the sound of a horn. Palindromes are words, phrases, or sequences that read the same forwards and backwards, and it's not possible to create one for the sound of a horn.