Guitar Strings Location
Physics Help– Waves?
I need help with the last two problems on my physics homework:
1) A piece of string 5.30 m long has a mass of 15.0 g. What must the tension in the string be to make the wavelength of a 125-Hz wave 120.0 cm?
2) The wave speed in a guitar string is 265 m/s. The length of the string is 63 cm. You pluck the center of the string by pulling it up and letting go. Pulses move in both directions and are reflected off the ends of the string.
a) How long does it take for the pulse to move to the string end and return to the center?
b) When the pulses return, is the string above or below its resting location?
c) If you plucked the sting 15 cm from one end of the string, where would the two pulse meet?
Thank you for your help!
1) For a frequency f of 125Hz and a wavelength λ of 1.20m we need a wave speed of v = λf
= 1.20*125 = 150m/s
but v = sqrt(T/μ) so T = v^2*μ = 150^2*0.015kg/5.30m = 63.7N
2) a) the t for each is d/v = 2*0.315m/265m/s = 2.38×10^-3s
b) since you pulled up at a node the string should be above the rest position
c) Let x be the distance from the 15cm end
So the distance for this end is 15 + x and for the other is (48 + 63 – x)
Equating these we get 15 + x = 111 – x
so x = (111 -15)/2 = 48cm
Liona Boyd – Adagio for Guitar and Strings