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

In summary, the string has a fundamental frequency of 100Hz and must have a tension of approximately 57.6N/m.
  • #1
naeblis
26
0
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.
 
Physics news on Phys.org
  • #2
naeblis said:
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
 
  • #3
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
naeblis said:
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.
 
  • #5
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
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.
 
Last edited:
  • #7
naeblis said:
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.
 

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

1. What is tension?

Tension is a pulling force that is exerted on an object or material.

2. How do I calculate tension?

Tension can be calculated by multiplying the mass of the object by the acceleration due to gravity and the length of the object. The formula is T = mgL, where T is tension, m is mass, g is acceleration due to gravity, and L is length.

3. What are the units for tension?

The units for tension are typically expressed in newtons (N) or pounds (lbs).

4. What is the significance of 100Hz in the calculation?

100Hz is the frequency at which the tension is being measured. This means that the tension is changing 100 times per second.

5. Can tension be negative?

Yes, tension can be negative if the object is being compressed instead of pulled. In this case, the tension would be considered a compressive force.

Similar threads

  • Introductory Physics Homework Help
Replies
2
Views
937
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
5
Views
993
  • Introductory Physics Homework Help
Replies
4
Views
3K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
11
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
3K
  • Introductory Physics Homework Help
Replies
19
Views
963
  • Introductory Physics Homework Help
Replies
7
Views
2K
Replies
5
Views
2K
Back
Top