This sound is likely originally a 20th Century Fox sound effect and possibly an Major Records/Valentino sound effect called Bull Elephant Trumpeting, which can be found on Major Records - Sound Effects Volume 4 in 1958, except it is low-pitched. It first debuted in the 20th Century Fox film, The Roots of Heaven on October 15, 1958.
This sound is referred to as "The Sesame Street Elephant Trumpet" due to being used as a phenomenon in Sesame Street, often heard heavily in this show, along with AT043801, and AT043901. This can be heard in high and low pitches. This sound is often used for Fluffy, the elephant that lives in Oscar's trash can. This also was used for many elephants in this show. They used this a lot, even in today's era of Sesame Street. The 1st time it was used on Sesame Street was in a skit featuring Grover and Simon Soundman at Charlie's Restaurant (though, it was more high pitched).
Elmo's World (Heard once in "Exercise", "Flowers, Plants and Trees", and "Weather", in a normal pitch, "Sleep" and "Feet" in a low pitch and "Wild Animals", in a high pitch.)
Johnny Bravo (Heard once in "Double Vision" and "The Hunk at the End of This Cartoon".)
Johnny Test (Heard once in "Here, Johnny! Here Boy!", "Johnny's Keys to Success" and "Johnny on the Clock".)
JoJo's Circus (Heard once in "Try These On for Boing!", "Seal Fright", "The Un-Average Day", "A New Twist", "My Dinner with the Tightropes" and "Charlie the Clown Baby Returns".)
Jungle Cubs (Heard once in "Trunks for the Memories".)
Jungle Junction (Used sometimes for Ellyvan's trumpet sounds.)
KaBlam! (Heard once in "The Off-Beats: Sweepstakes".)
Little Bill (Heard thrice in "The Zoo" and heard once in "Elephant on the Loose", "Number One on Honeywood Street" and "The Car Keys".)
Little Einsteins (Heard a few times in a normal pitch in "Jump for Joey", once in "Annie, Get Your Microphone!", "Animal Snack Time" and "Fire Truck Rocket", and heard more than once in a higher and normal pitch in "Little Elephant's Big Parade".)
Pinky Dinky Doo (Heard once in "Pinky and the Pink Phenomenon" when Pinky screams "PIIINK!!!", and "Pinky Dinky Doo and the Cloud People" when Pinky and Mr. Guinea Pig are hiding in the blanket. Also heard in "Dragon Needs a Sippy Cup" and "Boom Sonic Boom!".)
Samurai Jack (Heard once in a normal pitch in EPISODE LI: "Young Jack in Africa"; twice in a high pitch and once in a higher pitch in EPISODE XXVII: "Chicken Jack".)
Sesame Street (Heavy use of this sample up to the 2000s. When an elephant is in this show, this sound can often be heard.)
Sheep in the Big City (Heard twice in "My, How Ewe Have Changed!" and once in "Be Still My Bleating Heart", "A Star is Shorn", "Wish You Were Shear" and "The Wool is Not Enough".)
Sidekick (Heard once in "The Dingalingish Patient".)
SpongeBob SquarePants (Heard once in "Bubblestand" (low pitched), "Walking Small", "I'm with Stupid", "The Secret Box", "No Weenies Allowed", "Love That Squid", "Big Sister Sam", "Old Man Patrick" and "Who R Zoo?".)