  New interactions of neutrinos can stop them from free streaming even after
the weak interaction freeze-out. This results in a phase shift in the cosmic
microwave background (CMB) acoustic peaks which can alleviate the Hubble
tension. In addition, the perturbations in neutrinos do not decay away on
horizon entry and contribute to metric perturbation enhancing the matter power
spectrum. We demonstrate that this acoustic phase shift can be achieved using
new interactions of standard left-handed neutrinos with dark matter without
changing the number of effective relativistic degrees of freedom. Using Planck
CMB and the WiggleZ galaxy survey $ (k\le 0.12 h \ {\rm Mpc}^{-1} ) $ data, we
demonstrate that in this model the Hubble tension reduces to approximately $
2.1 \sigma$. Our model predicts potentially observable modifications of the CMB
B-modes and the matter power spectrum that can be observed in future data sets.
