XQUERY - How to use the sql:variable in 'value()' function?

Question

The query below is trying to select a child node of a given Node. How do I use a variable instead of hard coding the child node such that I can pass them as parameters in a SProc?

declare @T table(XMLCol xml)
insert into @T values
('<Root xmlns="http://tempuri.org" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <Elem1 type="T1">
    <Name type="string" display="First name">John</Name>
    <TimeZone display="Time zone">
      <children>
      <DisplayName type="string" display="Display name">GMT Standard Time</DisplayName>
      <HiddenName type="string" display="Hidden name">GMT</HiddenName>
      </children>
    </TimeZone>
  </Elem1>
</Root>') 

declare @Node varchar(50)
set @Node = 'TimeZone'

select N.value('(children/DisplayName)[1]', 'varchar(100)') as Value
from @T as T
  cross apply T.XMLCol.nodes('//*[local-name()=sql:variable("@Node")]') as X(N)

Answer 1

declare @T table(XMLCol xml)
insert into @T values
('<Root xmlns="http://tempuri.org" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
  <Elem1 type="T1">
    <DisplayName type="string" display="Display name">No this</DisplayName>
    <Name type="string" display="First name">John</Name>
    <TimeZone display="Time zone">
      <children>
        <DisplayName type="string" display="Display name">GMT Standard Time</DisplayName>
        <HiddenName type="string" display="Hidden name">GMT</HiddenName>
      </children>
    </TimeZone>
  </Elem1>
</Root>') 

declare @Node1 varchar(50)
set @Node1 = 'TimeZone'

declare @Node2 varchar(50)
set @Node2 = 'DisplayName'

select N2.Value.value('.', 'varchar(100)') as Value 
from @T as T
  cross apply (select T.XMLCol.query('//*[local-name()=sql:variable("@Node1")]')) as N1(Value) 
  cross apply (select N1.Value.query('//*[local-name()=sql:variable("@Node2")]')) as N2(Value)

Answer 2

declare @Node varchar(50)
set @Node = 'TimeZone'
declare @ChildName varchar(50)
set @ChildName='HiddenName'

;WITH XMLNAMESPACES(DEFAULT 'http://tempuri.org')
select N.value('.', 'varchar(100)') as Value
from @T as T
  cross apply T.XMLCol.nodes('//*[local-name()=sql:variable("@Node")]/children/*[local-name(.)=sql:variable("@ChildName")]') as X(N)