When a trumpet player sees "muted" over a section of music, without any further description, then the composer is calling for the trumpeter to put a straight mute inside his bell. Straight mutes are the simplest kind of mute a trumpet player can use, and little more than a hollow cone with an open tip that faces into the bell of the trumpet. This serves to subdue the sound of the trumpet while making the subdued sound have a slightly nasal tone. The specific tone will vary depending on the materials which the manufacturer used to make the mute.
A trumpet baffle, also known as a Harmon mute, produces a buzzing sound at a higher pitch than trumpets usually play. While the straight mute is a cone with a closed bottom, the baffle is designed for sound to travel through its curved -- or baffled -- interior then through an outward-facing hole to the audience. Depending on the sound the composer or player wants to achieve, baffle mutes come with a stem that can go into this hole to subdue the sound.
Both the baffle and straight mute use cork strips to stick inside the trumpet's bell while the trumpeter plays. However, the straight mute only uses a few vertical strips of cork. This causes sound to flow into the mute as well as around the mute. The baffle, however, has a horizontal strip of cork that creates a seal around the mute. This causes all the sound to go through the baffle. This is necessary for the baffle to produce its distinctive sound, and requires the trumpet player to blow harder than he normally would to force the wind through the baffle.
Straight mutes are used in a variety of different musical areas, from jazz to classical symphonic compositions. Trumpet baffles are used more exclusively in jazz and big band compositions. The trumpet baffle, with its open end, lends itself to a greater variety of sound than the closed straight mute. In addition to the use of the baffle's stem to change the tone, performers can also cup their hand over the opening to further modify the sound the muted trumpet will produce.