MySQL table optimization to speed up queries - php

Question

I have a big mysql table ('d_operations') with more than 2 million records (and more to come). I have written a PHP webpage that shows a chart with the number of operations in a day for each half an hour (0:00 0:30 1:00 1:30 ... 23:59).
It works great but takes too much time to get the results so I am wondering if my table and queries could be optimized.
For each half an hour in a day I do a select query asking MySQL for the number of operations done in that period of time.
This takes more than a minute to finish!
This is the table schema:
mysql> describe d_operations;
+-----------+------------------+------+-----+---------+----------------+
| Field | Type | Null | Key | Default | Extra |
+-----------+------------------+------+-----+---------+----------------+
| idx | int(11) unsigned | NO | PRI | NULL | auto_increment |
| system_id | int(11) | YES | | NULL | |
| dev_id | varchar(17) | YES | | NULL | |
| name | varchar(17) | YES | | NULL | |
| nond | smallint(6) | YES | | NULL | |
| is_new | smallint(6) | YES | | NULL | |
| tstamp | int(10) unsigned | YES | | NULL | |
+-----------+------------------+------+-----+---------+----------------+
I have a auto_increment primary key, that doesn't seem to help in the queries. The rest of the fields can be repeated (a device can do several operations in that period of time and it can be rows with the same tstamp).
tstamp is UNIX timestamp
This is how I do the queries in PHP:
for($i=$GLOBALS['init_hour'];$i<=($GLOBALS['end_hour']-1800);$i+=1800){
$n=$i+1800;
$sql="SELECT count(*) as num from d_operations where (tstamp >= $i and tstamp < $n);";
$r=mysqli_query($GLOBALS['con'],$sql);
$row = mysqli_fetch_row($r);
$values = ($i == $GLOBALS['init_hour']) ? $row[0] : $values.",".$row[0];
$GLOBALS['a_average'][$i]=$row[0];
}
In the worst case, I loop through every half an hour in that day, that is 48 queries.
This is the MySQL explain command:
mysql> explain select count(*) as num from d_operations where (tstamp >= 1464739200 and tstamp < 1464825599);
+----+-------------+--------------+------+---------------+------+---------+------+---------+-------------+
| id | select_type | table | type | possible_keys | key | key_len | ref | rows | Extra |
+----+-------------+--------------+------+---------------+------+---------+------+---------+-------------+
| 1 | SIMPLE | d_operations | ALL | NULL | NULL | NULL | NULL | 2215384 | Using where |
+----+-------------+--------------+------+---------------+------+---------+------+---------+-------------+
1 row in set (0.00 sec)
Is there a more efficient way for doing this? (table definition, MySQL query optimization...)
Thanks

Answer 1

As Jon Stirling and Mark Baker suggested, the solution was as simple as creating an index for the tstamp column:
ALTER TABLE d_operations ADD INDEX ts_index(tstamp);
Thanks!