When a big balloon is popped, it produces a deeper sound compared to a smaller balloon due to differences in their vibrational frequencies. The pitch or perceived frequency of a sound is determined by the rate of vibration of the object producing the sound. In this case, the balloon acts as a resonating chamber, and the sound it produces when popped is influenced by the size and shape of that chamber.
A larger balloon has more internal space, which allows for a larger resonating chamber. When the balloon is popped, the sudden release of pressurized air creates a sound wave that resonates within the chamber. The larger volume of the big balloon causes the sound wave to have a longer wavelength and a lower frequency, resulting in a deeper or lower-pitched sound.
On the other hand, a smaller balloon has a smaller resonating chamber. When it is popped, the resulting sound wave has a shorter wavelength and a higher frequency, leading to a higher-pitched sound.
In summary, the size of the balloon affects the size of the resonating chamber, which in turn influences the wavelength and frequency of the sound produced when the balloon is popped. A bigger balloon produces a deeper sound due to its larger resonating chamber, while a smaller balloon produces a higher-pitched sound due to its smaller resonating chamber.