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 f , in a string of length L and under tension T , n antinodes are set up in the string. (a) If the length of the string is doubled, by what factor should the frequency be changed so that the same number of antinodes is produced? (b) If the frequency and length are held constant, what tension will produce n + 1 antinodes? (c) If the frequency is tripled and the length of the string is halved, by what factor should the tension he 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 f , in a string of length L and under tension T , n antinodes are set up in the string. (a) If the length of the string is doubled, by what factor should the frequency be changed so that the same number of antinodes is produced? (b) If the frequency and length are held constant, what tension will produce n + 1 antinodes? (c) If the frequency is tripled and the length of the string is halved, by what factor should the tension he changed so that twice as many antinodes are produced?
Solution Summary: The author explains that the frequency of the vibrator should be changed by a factor of 12 so that same number of '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 f, in a string of length L and under tension T, n antinodes are set up in the string. (a) If the length of the string is doubled, by what factor should the frequency be changed so that the same number of antinodes is produced? (b) If the frequency and length are held constant, what tension will produce n + 1 antinodes? (c) If the frequency is tripled and the length of the string is halved, by what factor should the tension he changed so that twice as many antinodes are produced?
A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), where x and y are in meters and t is in seconds. The linear mass density of the string is a = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same frequency, and same linear mass density, then the new power of the wave is?
Chapter 18 Solutions
Physics for Scientists and Engineers, Technology Update (No access codes included)
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