Calculating Linear Density of a Standing Wave: Solving for Lambda

[lionely]

Standing waves are set up on the apparatus. Here the distance from P to Q is L=1.20m
and the oscillator is set to a frequency 120Hz. A standing wave appears when the mass of the hanging block is 286.1g or 447.0 grams, but not for any intermediate mass. What is the linear density of the string?

I know

μ = tension/v^2 = tension/(λ^2 f^2)

I need to get lambda but I don't know how to.

help is greatly appreciated!

 

[TheShrike]

I'm not quite sure of the experimental set-up you have, but think about the number of nodes of the standing wave. It can be linked to the wavelength.

 

[lionely]

The thing is I don't know the # of nodes.

 

[TheShrike]

Just making sure, but does that also mean you don't know whether the standing wave is occurring at the fundamental frequency or at one of the overtones?

 

[lionely]

Yeah.

 

[haruspex]

If L is the length of the string, what is the wavelength of the nth harmonic?

 

[lesieux]

You know that nodes are separated by a distance which is half the wavelength therefore L=n*lambda/2

 

[Philip Wood]

Do you agree that $\lambda = \frac{2L}{n}$ in which L is the string length and n is the number of antinodes? Substitute for $\lambda$ into the equation you already have, and make n the subject. You can then write the equation for n = n₁ (say) for the tension corresponding to 447.0 gram, and another for n = n₁ +1, for the tension corresponding to 286.1 gram. Take it from there...

 

[jtbell]

Duplicate threads have been merged.