Calculate Tension of Mass 2.4x10^-3 kg & Length 0.60m @ 100Hz

[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.

 

[OlderDan]

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.

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

 

[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.

 

[OlderDan]

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.

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.

 

[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?

 

[Tony Zalles]

Hi,

Your given:

m = mass
(fn) = fndamental frequecny

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

Ok so let's 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)

rearrange for (Ft) and there's your answer.

-Tony Zalles.

 

[OlderDan]

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?

Throw in some proper units and I think you have it.