Wave speed is proportional to
[Tension/(linear density)]^1/2
Linear density is the density per unit string length. String A has 1/2 the tension and (0.59/1.3)^2 = 0.206 times the linear density of String B.
The wave speed ratio is therefore
VA/VB = sqrt [(1/2)/0.206] = 1.558
The length does not matter for the wave speed, but does help determine the resonant standing wave frequencies.
Please someone help me I'm desperate!!!!
Two steel guitar strings have the same length. String A has a diameter of 0.59 mm and is under 420.0 N of tension. String B has a diameter of 1.3 mm and is under a tension of 840.0N .
Find the ratio of the wave speeds,VA/VB , in these two strings.
3 answers
wave speed= sqrt (tension/(mass/length))
now, mass/length in the strings (assuming same material) is proportional to area, or diamter^2
wavespeed=Constant*sqrt (tension/diameter^2)
so
wavespeed1/wavespeed2= sqrt(Tension1/tension2 * diameter2^2/diameter1^2)
now, mass/length in the strings (assuming same material) is proportional to area, or diamter^2
wavespeed=Constant*sqrt (tension/diameter^2)
so
wavespeed1/wavespeed2= sqrt(Tension1/tension2 * diameter2^2/diameter1^2)
Very close. Remember to change mm to meters. Greatly effects answer.
Va/Vb = sqrt[(Tension1/Tension2)*(Diameter2^2/Diameter1^2)]
Va/Vb = sqrt[(420/840)*((5.9E-4)^2/(1.3E-3)^2)]
Va/Vb = sqrt[(Tension1/Tension2)*(Diameter2^2/Diameter1^2)]
Va/Vb = sqrt[(420/840)*((5.9E-4)^2/(1.3E-3)^2)]