Stationary wave question

1. Aug 7, 2013

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!!

Last edited: Aug 7, 2013
2. Aug 7, 2013

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.

3. Aug 7, 2013

lionely

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

4. Aug 7, 2013

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?

5. Aug 7, 2013

Yeah.

6. Aug 7, 2013

haruspex

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

7. Aug 8, 2013

lesieux

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

8. Aug 8, 2013

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...

9. Aug 8, 2013