A standing wave on a tight string experiment is set up in thelaboratory. The str

Question

A standing wave on a tight string experiment is set up in thelaboratory. The string is stretched between two posts that are1.5 m apart. When the string is vibrated at a frequency of 60Hz, a standing wave of four loops can be seen. The linear massdensity of the string is 1.5 g/m. A. What is the wave speed of the standing wave? B. What is the tension in the string? A standing wave on a tight string experiment is set up in thelaboratory. The string is stretched between two posts that are1.5 m apart. When the string is vibrated at a frequency of 60Hz, a standing wave of four loops can be seen. The linear massdensity of the string is 1.5 g/m. A. What is the wave speed of the standing wave? B. What is the tension in the string? A. What is the wave speed of the standing wave? B. What is the tension in the string?

Explanation / Answer

    Length of the string, L = 1.5 m     Frequency, f = 60 Hz     No. of loops, n = 4     Length of each loop, L' = /2           (where = wavelength )     Total length of all loops = n L'                                        = 4 * ( / 2 )                                        = 2     But, Total length , L = 1.5 m                        2 = 1.5 m     Wavelength, = 0.75 m    Linear mass density, = 1.5 g/m                                      = 1.5 X 10 -3 kg/m     (a)     Speed of the wave in the string, V = f                                                        = 60 * 0.75                                                        = 45 m/s     (b)     Velocity of transverse wave, V = ( T / )     Tension, T = V 2                     = 45 2 * 1.5 X 10 -3                     = 3.04 N

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