A stretched string, clamped at its ends, vibrates at a particular frequency.To double that frequency, one can change the string tension by a factor of:
A)2
B)4
D)1/2

Question

A stretched string, clamped at its ends, vibrates at a particular frequency.To double that frequency, one can change the string tension by a factor of:
A)2 
B)4 
D)1/2

Quizplus · Accepted Answer

The frequency of vibration of a stretched string is directly proportional to the square root of its tension. So, to double the frequency, we need to increase the tension by a factor of 4. This can be seen from the formula: f1/f2 = sqrt(T1/T2), where f1 and T1 represent the initial frequency and tension, and f2 and T2 represent the new frequency and tension. Solving for T2/T1, we get T2/T1 = (f2/f1)^2 = 2^2 = 4. Therefore, the string tension needs to be changed by a factor of 4 to double the frequency of vibration.

A Stretched String, Clamped at Its Ends, Vibrates at a Particular