A nylon string has a linear density of 7.2g/m and is under a tension of 150N. The fixed supports are 90cm apart. The string is oscillating in the standing wave pattern. Find a)speed b)wavelength c) frequency
v=sqr(F/u(linear density)
v=sqrt(150N/7.2g/m)
= 4.56m/s
b) wavelength = 2L/3
= .6
The formular is =2L/n
n= nodes. The pictures shows three nodes in the standing wave pattern.
c) v= wavelength * frequency
4.56=.6 *f
f=7.6 Hz
Shouldn't linear density be changed to kg/m when determining velocity?
Wavelength should be twice the 90cm, shouldn't it? The end points determine the nodes, and between nodes it should be 1/2 wavelength.
wavelength= 2(.9m) I don't know why you chose n=3, I would have thought n=1 for the fundamental.
You are correct, when determining velocity, the linear density should be changed to kilograms per meter (kg/m). The formula for velocity, v, is v = sqrt(F/u), where F is the tension in newtons and u is the linear density in kg/m. So to calculate the velocity, it should be v = sqrt(150 N / 0.0072 kg/m) = 128.87 m/s. Thank you for catching that mistake.
Regarding the wavelength, you are also correct. In the formula wavelength = 2L/n, L represents the distance between the fixed supports, which is 90 cm or 0.9 m in this case. Since you mentioned that there are three nodes in the standing wave pattern, the correct value for n would be 3. Therefore, the wavelength would be 2(0.9 m) / 3 = 1.2 m. I apologize for the error in my previous response.
Thank you for pointing out these mistakes, and I apologize for any confusion caused.