Answer :
Final answer:
The string should be brushed 60 cm from one end to alter its fundamental frequency from 124 Hz to 186 Hz, making option 1 the correct answer.
Explanation:
The student has asked where a string should be brushed to alter its fundamental frequency from 124 Hz to 186 Hz. The length of the string is 90 cm. Since the frequency is inversely proportional to the length when tension and mass per unit length are constant, we can use the ratio of the frequencies to find the new length that will have the 186 Hz fundamental frequency. The calculation is as follows:
(Length_{new}) / (Length_{original}) = (Frequency_{original}) / (Frequency_{new})
L_{new} / 90 cm = 124 Hz / 186 Hz
L_{new} = 90 cm × (124/186)
L_{new} ≈ 60 cm
This means the string must be brushed or plucked 60 cm from one end to produce a fundamental frequency of 186 Hz. The correct answer is option 1.
