use shell variables in sed

input=abc.wav
i=0
while test $i != 10
do
   echo "run case $i
   tag=`expr output-foo-$i`
   output=`echo $input | sed -e "s/^\(.*\)\.wav$/\1-$tag\.wav"`
   ./foo.bin -v -e -E $i -o $output $input
done

Here instead of

sed -e 's/^\(.*\)\.wav$/\1-$tag\.wav'

Use

sed -e "s/^\(.*\)\.wav$/\1-$tag\.wav"