Question

If the total mass hanging on one end of the string that creates the tension in the string is 1.20 kg, what is the mass density (mass per unit length) ? of the string? L = 0.800 m, frequency of 24.0 Hz.

Answer 1

mass =1.2kg

l = 0.8m

mass density = m/l

= 1.2/0.8

= 1.5 kg/m

Answer 2

The gravity force on the mass supplies the tension

m . g = 1.2 * 9.81 = 11.772 N

m = 1.2 kg

Increasing the mass will increase the tension, which will increase the velocity. With a fixed frequency this means that the wavelength must increase.
The maximum wavelength possible is 1.6 m

so the maximum speed ( to produce a coherent standing wave ) = 24 . 1.6 = 38.4 m/s

38.4 = ? T / mu

mu^2 = 11.772/1474.56

mu = 0.089 kg/m

Answer 3

frequency of mass loaded string is given by

$f = \frac{1}{2L}\sqrt{\frac{T}{\mu }}$

here tension T= Mg = 1.2 * 9.8 =11.76N and length of string L = 0.800m, frequency f = 24Hz

so $24 = \frac{1}{2*0.800}\sqrt{\frac{11.76}{\mu }}$

$so linear density \mu = 0.007975kg/m$