Question

A string is stretched between two supports that are L = 0.9 m apart. It resonates at a frequency of f = 410 Hz with a standing wave pattern that has two nodes between the two supports.
(a) Find the wavelength λ in meters.
(b) Suppose that the tension, T, in the string is increased by a factor of 4. What is the new frequency f' in Hz if the string vibrates with the same standing wave pattern as in the drawing above?
bobpursley
The wire length is one half wavelength

wave speed is proportional to the square root of tension, so wave speed is doubled here.

f*lambda=speed, so if lambda is constant, speed doubled, f must...
I got the wavelength to be (2/3)L which gives you .6 and that's correct, but I can't get the second part right

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