Guitar string frequency and tension calculation

[buffgilville]

1) The fundamental of a guitar string whose ends are a distance 0.55m apart has a frequency 283.23 Hertz. If the linear density of the string is 0.01 kG/meter, the tension of the string (in Newtons) is

T=f^2 * linear density * wavelength^2
f=283.23
linear density = 0.01
how do find the wavelength? I know that wavelength = velocity/frequency but the velocity of the wave on the string is not given. How does the fact that the guitar string's ends being 0.55m apart have to do with the tension of the string?


2) A heavy uniform rope is hanging freely from one end. The speed of a wave a distance 0.67 from the bottom of the rope (in meters/sec) is

how do I do this type of problem?

 

[spacetime]

(1) Since this is the fundamental frequancy, the string is vibrating with no nodes in between. So,

$$\lambda=2L$$

(2) Tension at distance x from bottom is $$\frac{Mxg}{L}$$ where M is the mass of the rope and L is the length.
So, divide it by the mass per unit length M/L, take the square root and you get the speed.

spacetime
www.geocities.com/physics_all

 

[buffgilville]

Thanks spacetime!