Conduct Activity 10.1 once again with a thick rubber band and then with a thin rubber band. Does the thin rubber band vibrate faster than the thick rubber band? If yes, how do the frequency and time period of the sound produced by the thin rubber band differ from that of the thick rubber band?
Yes, the thin rubber band vibrates faster than the thick rubber band when plucked under similar conditions.
Because the thin rubber band vibrates faster, it completes more oscillations in a given time. Therefore, the frequency of the sound produced by the thin rubber band is higher than that of the thick rubber band.
Conversely, since it takes less time to complete a single oscillation, the time period of the sound produced by the thin rubber band is shorter than that of the thick rubber band.
Explanation
The question explores how the thickness of a vibrating material affects its vibration speed, frequency, and time period. A thin rubber band has less mass and thus vibrates more rapidly than a thick one. Since frequency is the number of oscillations per unit time, faster vibration results in a higher frequency. Time period, being the time taken for one complete oscillation, is inversely related to frequency; hence, a faster vibration means a shorter time period.