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------------------------------------------------ A string under a tension of 920 N has a fundamental mode of vibration with a frequency of 542 Hz. What will be the frequency of the fundamental mode if the tension is increased by 18%?

a.) 755 Hz
b.) 640 Hz
c.) 589 Hz
d.) 97.6 Hz

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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