Quintupling the tension in a guitar string will change its natural frequency by what factor? B)1 D)5 E)5²

Question

Quizplus · Accepted Answer

The natural frequency of a guitar string is directly proportional to the square root of its tension. Quintupling the tension means multiplying it by 5. Therefore, the new frequency will be the square root of 5 times the old frequency. This can be simplified as sqrt(5)*sqrt(frequency) or sqrt(5*frequency). Hence, the factor by which the natural frequency changes is sqrt(5) which is approximately 2.24. Choice C, 11ea800b_1910_5e3c_846e_657262fd77bd_TB6864_11, is the closest approximation to this value.

Quintupling the Tension in a Guitar String Will Change Its