Answer :
The frequency of the fundamental mode of vibration when the tension is increased by 18% is approximately 588.6 Hz.
The frequency of the fundamental mode of vibration of a string is directly proportional to the square root of the tension.
Let's calculate the new tension after increasing it by 18%:
New tension = 920 N + (18/100) * 920 N = 1085.6 N
Now, let's calculate the new frequency using the new tension:
New frequency = √(New tension / Original tension) * Original frequency
New frequency = √(1085.6 N / 920 N) * 542 Hz
Calculating the new frequency:
New frequency ≈ √(1.18) * 542 Hz ≈ 1.086 * 542 Hz ≈ 588.6 Hz
Therefore, the frequency of the fundamental mode of vibration when the tension is increased by 18% is approximately 588.6 Hz.
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