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

Quizplus · Accepted Answer

The fundamental frequency of a stretched string is given by:

f = (1/2L) * sqrt(T/µ)

where L is the length of the string, T is the tension, and µ is the linear density of the string.

To double the fundamental frequency, we need to double the value of f. From the above equation, we can see that f depends on the square root of T. Therefore, to double f, we need to quadruple the value of T. Hence, the answer is B, i.e., 4.

A Stretched String, Clamped at Its Ends, Vibrates in Its