In يَنْعِقُ, nūn sākinah is followed by ʿayn (ع), so the n is clear. In عَذَابٌ أَلِيمٌ, the tanwīn is followed by hamzah (ء), so its n-sound remains distinct during connection.
One is written nūn and the other tanwīn, yet both follow exactly the same trigger: a throat letter.
Practice note: do not suppress the n-sound, but do not exaggerate its length.
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The source’s iẓhār examples
Sākin Nūn & Tanwīn — Iẓhār, Idghām, Qalb and Ikhfāʾ
In يَنْعِقُ, nūn sākinah is followed by ʿayn (ع), so the n is clear. In عَذَابٌ أَلِيمٌ, the tanwīn is followed by hamzah (ء), so its n-sound remains distinct during connection.
One is written nūn and the other tanwīn, yet both follow exactly the same trigger: a throat letter.
Practice note: do not suppress the n-sound, but do not exaggerate its length.