Piano string tension needed to raise middle C from 249 Hz to 261.6 Hz

[Phymath]

well here's the problem: A piano tuner detects that the "middle C" note, which should be 261.6 Hz, is too low by 12.6 Hz. If the original tension was 754 N, what must it be adjsuted to so the note plays the correct frequency?

however i have no idea where to even start?! i got these formulas but i was never given a 4th value like the density (mu) or the velocity of the note in the wire where to go!

$$v = \sqrt{\frac{T}{\mu}}$$
$$v = \lambda f = \frac{\lambda}{t}$$ where t is the period, and T is the tension in the string

as well as this one.. i think its a porportionalitly question I am not sure though please help me even get started

A string is made of two materials of different mass per unit length, 2.31 g/m on the left and 3.25 g/m on the right, connected together at the center. If the wavelength of the wave on the left segment is 21.7 m, what is the wavelength on the right?

 

[M.Hamilton]

i think its a porportionalitly question I am not sure though

I'll take a crack at the first problem...I’ve got a bit of a cold, but I think your right. The first question is a proportionality question. If you know that T1=754N and F1=261.6Hz then perhaps an equality would solve this one, you already know what F2 is, now all you need is to solve for T1.

Merle

 

[Phymath]

agreed as possibly the last problem is the same, however these problems are typically not like that but ill give it a shot thanks