A standing wave pattern is created on a string with mass density ? = 3.1 Now the
ID: 1297917 • Letter: A
Question
A standing wave pattern is created on a string with mass density ? = 3.1
Now the hanging mass is adjusted to create the 2nd harmonic. The frequency is held fixed at f = 67 Hz. What is the wavelength of the wave? m 6) What is the speed of the wave? m/s 7) What is the tension in the string? N 8) What is the mass hanging on the end of the string? kg 9) Keeping the frequency fixed at f = 67 Hz, what is the maximum mass that can be used to still create a coherent standing wave pattern? kg A standing wave pattern is created on a string with mass density ? = 3.1 ?? 10-4 kg/m. A wave generator with frequency f = 67 Hz is attached to one end of the string and the other end goes over a pulley and is connected to a mass (ignore the weight of the string between the pulley and mass). The distance between the generator and pulley is L = 0.59 m. Initially the 3rd harmonic wave pattern is formed. 1) What is the wavelength of the wave? m 2) What is the speed of the wave? m/s 3) What is the tension in the string? N 4) What is the mass hanging on the end of the string? kg 5)Explanation / Answer
f=nv/2L -> v=2Lf/n , n=3
v= 2*0.59*67/3= 26.35m/s
(1) ?=v/f = 26.35/67= 0.393m]
(2) v= 26.35[m/s]
(3) v=?(T/?) -> T=v^2*?
T= 26.35^2*3.1*10^-4 = 0.215[N] approx.
(4) F=ma -> m=F/a , as a=9.8m/s^2
m= 0.215/9.8= 0.0219= 2.19*10^-2[kg]
(6) v=2Lf/n , n=2
v= 2*0.59*67/2= 39.53m/s
(5) ?=v/f = 39.53/67= 0.59[m]
(7) T=v^2*? = 39.53^2*0.00031= 0.4844= 0.48[N]
(8) m=F/a = 0.4844/9.8= 0.04942= 4.94*10^-2[kg]
(9) n=1: for fundamental frequency
v=2Lf/n = 2*0.59*67/1= 79.06m/s
T=v^2*? = 79.06^2*0.00031= 1.9376N
m=F/a = 1.9376/9.8= 0.19771= 1.977*10^-1[kg]
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