A partially open window presents an opening 20cm wide.
What kind of sounds from outside will go across the room in a well-defined beam?
What kind will spread evenly throughout the room?
Roughly what frequency marks the boundary between the two cases?
To understand which sounds will go across the room in a well-defined beam and which ones will spread evenly throughout the room, we need to consider the phenomenon of diffraction and the concept of wavelength.
1. Sounds that will go across the room in a well-defined beam:
When a sound wave encounters an obstacle or a narrow opening, it tends to bend or diffract around the edges of the obstacle. This bending effect is more pronounced when the wavelength of the sound wave is comparable to the size of the opening. In the case of a partially open window with an opening of 20cm, if the wavelength of the sound is relatively large compared to the opening, the sound is more likely to pass through the window and continue in a well-defined beam across the room. Low-frequency sounds, such as those produced by large subwoofers or bass instruments, typically have longer wavelengths and are more likely to behave in this manner.
2. Sounds that will spread evenly throughout the room:
On the other hand, when the wavelength of the sound is relatively small compared to the opening, the sound wave tends to spread out in all directions after passing through the window. This spreading effect is more prominent when the opening is similar in size or smaller than the wavelength. High-frequency sounds, such as those produced by small tweeters or high-pitched instruments, typically have shorter wavelengths and are more likely to spread evenly throughout the room.
3. Frequency boundary between the two cases:
The boundary between the two cases where the sound behaves as a defined beam or spreads evenly is not fixed and can vary depending on the size of the opening. However, as a rough estimate, the boundary is often seen around the range of 1,000 to 2,000 Hz. Sounds above this frequency range tend to spread more evenly throughout the room, while sounds below this range might behave more like a defined beam. It's important to note that this is a general approximation and can vary based on specific conditions.
In summary, low-frequency sounds with longer wavelengths tend to pass through relatively narrow openings and propagate in a well-defined beam across the room. High-frequency sounds with shorter wavelengths, however, tend to spread evenly in all directions after passing through the opening. The boundary between the two cases is approximately in the range of 1,000 to 2,000 Hz.