Sound produced by the school bell is dependent on how the bell vibrates when it is hit. The particles of the medium start to vibrate when the bell is hit physically or mechanically. As the particles start to vibrate, there is disturbance caused in the waves. When the bell moves forward, it pushes the air particles in the front creating a region of high pressure which is known as compression. When the bell moves backward, a low pressure region is created which is known as rarefaction. The continuous formation of compression and rarefaction makes the sound of the school bell to propagate through the air.
Below is the video explaining what are sound waves and its oscillation: