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 A , 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, nA , length LA , tension TA , and linear density mB = 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 . (c) If the frequency and length are held constant, what tension TB will produce nA + 1 antinodes? (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?
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 A , 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, nA , length LA , tension TA , and linear density mB = 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 . (c) If the frequency and length are held constant, what tension TB will produce nA + 1 antinodes? (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?
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