Young friend asked: “Why only offer food to Crow in Shradhdh paksha?”
It is not fixed that you offer food to only crow. Crow represents the weaknesses you received in legacy. It is to tame the Crow-legacy received.
We do not only receive physical body as legacy but also other parts of body (Refer: Panchkoshiya Sharir) from maternal and paternal seeds.
Manomay Kosha of our ancestors may have imprints of wavering nature due to their limitations or circumstances (or any other mental disorder of varied degree). The crow or कौआ is your Manomay sharir’s legacy defect, which represents चलद्रष्टि (wavering mind) predominantly. Everyone suffers from चलद्रष्टि of different intensity. Vata + Tamas type suffer more.
This is the time to take care of this defect and overcome it.
Since we cannot imagine anything without reference, it is important to feed Crow during this time of the year so that we can be reminded about wavering nature of our mind and immediate control over it.
As long as offering is concerned, this is what Vayu Puran has to say:
After death, as per karmic account or गुप्तचित्र, we receive different गति. कोई देवता तो कोई पितर तो कोई प्रेत तो कोई प्राणी तो कोई वृक्ष बनता है.. कुछ न कुछ तो बनता ही है..या बनने के समयकी राह देख रहा होता है..(trapped in time).
So how really my tarpan reaches to my ancestors?
नाममंत्रास्तथा देशा भवान्तरगतानपि ।
प्राणिनः प्रीणयन्त्येते तदाहारत्वमागतान् ।।
देवो यदि पिता जातः शुभकर्मानुयोगतः ।
तस्यान्नममृतं भूत्वा देवत्वेऽप्युनुगच्छति ।।
मर्त्यत्वे ह्यन्नरूपेण पशुत्वे च तृणं भवेत् ।
श्राद्धान्नं वायुरूपेण नागत्वे ऽ प्युपतिष्ठति ।।
The food is not just physical form (अन्नमय). It is after ritual performed, layer of your मनोमय, प्राणमय, विज्ञानमय & आनंदमय शरीर. So based on the योनी where ancestor is right now, different form reaches to them by various cycles of transformation of पिंड offered.
यथा गोष्ठे प्रणष्टां वै वत्सो विन्देत मातरम् ।
तथा तं नयते मंत्रो जन्तुर्यत्रावतिष्ठते ।
नाम गोत्रं च मंत्रश्च दत्तमन्नं नयन्ति तम् ।
अपि योनिशतं प्राप्तांस्तृप्तिस्ताननुगच्छति ।।
The way calf finds out her mother out of 1000s of Gaiya(s), same way with proper नाम,गोत्र, श्रध्धा & मंत्र , whatever is offered, reaches to all different ancestors.