To determine the fundamental frequency of the stretched string, we need to understand the relationship between the observed frequency and the harmonics of the string's vibration.
1. Identify the Mode of Vibration:
- The problem states that the string vibrates in three equal segments when driven by a 480 Hz oscillator.
- When a string vibrates in three equal segments, it is vibrating in its third harmonic (or third mode of vibration).
2. Understand Harmonics:
- The fundamental frequency (first harmonic) is the lowest frequency at which the string can naturally vibrate.
- The second harmonic is twice the fundamental frequency.
- The third harmonic is three times the fundamental frequency, and so on.
3. Relate Observed Frequency to Harmonics:
- Since 480 Hz corresponds to the third harmonic of the string, we can deduce that the fundamental frequency is one-third of this value.
4. Calculate the Fundamental Frequency:
- We divide the observed frequency by 3 to find the fundamental frequency:
[tex]\[
\text{Fundamental frequency} = \frac{480 \text{ Hz}}{3} = 160 \text{ Hz}
\][/tex]
Thus, the fundamental frequency of the vibration for the stretched string is [tex]\( \boxed{160 \text{ Hz}} \)[/tex].
