Question

A standing wave is set up in a string of variable length and tension by a vibrator of variable frequency. Both ends of the string are fixed. When the vibrator has a frequency fA, in a string of length LA and under tension TA, nA antinodes are set up in the string.

(a) Write an expression for the frequency fA of a standing wave in terms of the number nA, length LA, tension TA, and linear density μA.

fA=

(b) If the length of the string is doubled to LB = 2LA, what frequency fB (written as a multiple of fA) will result in the same number of antinodes? Assume the tension and linear density are unchanged. Hint: Make a ratio of expressions for fB and fA.

fB=

(c) If the frequency and length are held constant, what tension TB will produce nA + 1 antinodes? (Use any variable or symbol stated above as necessary.)

TB=

(d) If the frequency is tripled and the length of the string is halved, by what factor should the tension be changed so that twice as many antinodes are produced?