# Homework Help: A string of mass

1. May 11, 2005

### naeblis

A string of mass 2.4 x 10 ^ -3 kg and length 0.60 meters vibrates transversely in such a way that its fundamental frequency is 100Hz. The tension on this string must be approximately _____.

any help with this would be appreciated, i am not quite sure what i have to do.

2. May 11, 2005

### OlderDan

Find the equation that relates frequency of vibration of a string to the tension and mass per unit length. You have all the information to need to use it

3. May 11, 2005

### naeblis

i've been trying to work it with

v = (<tension>/<linear mass density>)^(!/2)

where i get stuck is the v. how do i figure out the velocity of the wave from the frequency. i know v= (f)(lambda)

i worked

(f)(lambda) = (<tension>/<linear mass density>)^(!/2)

and got

tension = (40)(lambda^2)

but i am not sure how to figure out the wavelength or if i even can.

4. May 11, 2005

### OlderDan

The string is attached at both ends, and it is vibrating in its fundamental mode, or at least the frequency of its fundamental mode is given. You can figure out the wavelength of the fundamental mode from that information.

5. May 11, 2005

### naeblis

ok ok ok so f = n(v/2L) where n =1

so i have 100Hz = (v/(2)(0.60m))

therefore v = 120 Hz/m

and then i can say

120 = (F / .004)^(1/2)

F = 57.6?

6. May 11, 2005

### Tony Zalles

Hi,

m = mass
(fn) = fndamental frequecny

ok now we need the force of tension on the string.

Ok so lets work it out.

(fn) = v/(lambda)

[lambda = wavelength]

And for a string...

(lambda) = 2L

[L = length of string]

thus (lambda) = 2L

and........(fn) = v/(lambda)
which is..(fn) = v/(2L)

rearrange for v, therefore: (2L)*(fn) = v

[* = multiplied]

now i believe you remembered v = ((Ft)/(mu))^(1/2)

[mu = linear mass density = m/L]

thus v = ((Ft)/(m/L))^(1/2)

now from here set what we got for v earlier, v = (2L)*(fn)

equal to v = ((Ft)/(m/L))^(1/2)