Modify object in a JSON array that also contains strings

I have a JSON file like this:

{"header": "headername","arrays": ["a_string",    {"name": "foo","properties": [        {"type": "some_type1","url": "https://example.com","checksum": "d6fd580fe890b826250aa5d5a88bcdb28839cff4d447ba51536cda4ceae89c4e"        }      ]    },"another_string",    {"name": "bar","properties": [        {"type": "some_type2","url": "https://example.org","checksum": "d6fd580fe890b826250aa5d5a88bcdb28839cff4d447ba51536cda4ceae89c4e"        }      ]    }  ]}

I want to change properties block of the array whose name is foo. The expected output is:

{"header": "headername","arrays": ["a_string",    {"name": "foo","properties": [        {"type": "foo","url": "bar"        }      ]    },"another_string",    {"name": "bar","properties": [        {"type": "some_type2","url": "https://example.org"        }      ]    }  ]}

Something like .arrays[]| select(.name == "foo").sources |= [{"type" : "foo", "url" : "bar"}] results in jq: error (at <stdin>:26): Cannot index string with string "name"and .| select(.name == "foo").sources |= [{"type" : "foo", "url" : "bar"}] can parse it but changes nothing.