Askiitians Tutor Team
Last Activity: 5 Days ago
To determine which scenario would produce beats when two vibrating strings are under the same tension, we need to consider how beats are formed. Beats occur when two sound waves of slightly different frequencies interfere with each other, resulting in a fluctuation in sound intensity. Let's analyze each option to see which one leads to this condition.
Understanding the Options
Option (a): The wavelengths of their sounds differ slightly.
When two strings vibrate, the frequency of the sound produced is inversely related to the wavelength. If the wavelengths differ slightly, it implies that the frequencies are also slightly different. This difference in frequency is crucial for the formation of beats. Therefore, this option is valid.
Option (b): Their lengths differ slightly but their linear densities are the same.
The frequency of a vibrating string is determined by its length, tension, and linear density. If the lengths of the strings differ slightly but their linear densities are the same, the frequencies will also differ slightly. This scenario will also produce beats, as the slight difference in frequency will lead to the interference of the sound waves.
Option (c): Their linear densities differ slightly but lengths are the same.
In this case, if the lengths of the strings are the same but their linear densities differ, the frequencies will change due to the different mass per unit length. This difference in linear density will result in different frequencies, thus also producing beats. So, this option is also valid.
Summarizing the Findings
All three options can lead to the production of beats because they each create a situation where two sound waves of slightly different frequencies interfere with each other. Here’s a quick recap:
- Option (a): Different wavelengths lead to different frequencies, producing beats.
- Option (b): Different lengths with the same linear density result in different frequencies, also producing beats.
- Option (c): Different linear densities with the same length lead to different frequencies, resulting in beats.
In conclusion, all three scenarios—(a), (b), and (c)—would produce beats when two vibrating strings are under the same tension. Each option creates a condition where the frequencies of the sound waves differ slightly, allowing for the interference that characterizes beats.
