Question

A spring of length 6.0 m is stretched between two walls at a tension of 12 N, as shown below. On the diagram above, draw the third harmonic. What is the wavelength of the third harmonic? If you measure the frequency of the third harmonic to be 15.0 Hz then what is the mass of the spring?

Answer 1

A)

spring

B)

The equation for wavelength of the third harmonic is

$3\left ( \frac{\lambda}{2} \right ) =L$

$\lambda =\frac{2 L}{3} = \frac{2(6)}{3} = 4 m$

c) The equation for the speed is

$V = f \lambda = (15 Hz)( 4 m) = 60 m/s$

The equation for the mass of the spring is

$V = \sqrt{\frac{T}{m/L}}$

$V^2 = \frac{T}{m/L}$

$m = \frac{TL}{V^2} = \frac{(12)(6)}{60^2} = 0.02 kg\Rightarrow 20 grams$