Final answer:
To determine the frequency that sets up five segments in a standing wave on a string, we can use the fact that frequency is directly proportional to the number of segments (antinodes). With four segments at 480 Hz, each segment represents 120 Hz. Therefore, for five segments, the frequency is 600 Hz.
Step-by-step explanation:
The question is asking about the relationship between the frequency of a standing wave and the number of segments (antinodes) that appear between the fixed ends of a vibrating string. Given that a frequency of 480 Hz sets up a standing wave with four segments, we can determine what frequency will set up five segments.
In a string fixed at both ends, standing waves are formed at frequencies that are proportional to the number of segments (antinodes). The relationship between the frequency (f) and the number of segments can be described by the equation:
f = n(v/2L)
Where:
- n is the number of segments (or antinodes)
- v is the speed of the wave on the string
- L is the length of the string
Since the speed of the wave and the length of the string remain constant, the frequency is directly proportional to the number of antinodes.
If the string originally has four segments at 480 Hz, one segment corresponds to 480 Hz / 4 = 120 Hz. Therefore, five segments would correspond to 120 Hz * 5 = 600 Hz.
The correct answer is (c) 600 Hz.