Frequency of a standing wave on a string

In summary, the problem involves a 50m string with mass 0.0175 kg and a mass of 0.45 kg attached, creating a 4.41 N tension. The waves travel at 112 m/s, according to the teacher's answer sheet. However, using the given data, the speed should be 159 m/s. The problem also involves finding the frequency of the string vibrator, but the given answer of 187 Hz does not match the calculations. After further discussion and clarification, it is determined that the length of the string in the diagram is actually 1.2m and not 50m, leading to the correct answer of 187 Hz using the equation f=v/λ and a wavelength of
  • #1
physicsfun88
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0

Homework Statement



a 50m length of string with mass 0.0175 kg has waves traveling at 112 m/s. There is a mass attached to the string, 0.45 kg that is creating a 4.41 N tension. What is the frequency of the string vibrator?

Homework Equations


v=f*λ
f= [√T/(m/L)]/2L

The Attempt at a Solution


I can't for the life of me get to the right answer, i know that it is 187 Hz, but I'm just not doing the math right or something like that.
 
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  • #2
The problem statement appears to be inconsistent. The speed of a wave on a string is

√(T/(m/L)) which yields 159 m/s using the data given. Yet the problem states that the speed

is 112 m/s. :confused:

[OOPS, the speed does in fact come out to be 112 m/s. Sorry!]

But something still seems strange. The formula you give for f is for the fundamental frequency of a standing wave (right?). Using L = 50 m yields 1.12 Hz. This is a very low frequency due to the string being very long. Is there any information given that would allow you to determine which harmonic the string is vibrating in? The numbers seem a little weird to me.
 
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  • #3
I'm not getting that same answer. T=4.41 m=0.0175 kg and L=50. which comes to 112.25. This is a worksheet from a teacher, I am a tutor, and the teacher for this student teaches wildly away from the book, so I am trying to find the simplest way to do this. His answer sheet says 112 for the speed, he rounded down. then knowing all of that information, asks to find the frequency. I can't find, even going backwards, any equation that will get 187 Hz.
 
  • #4
I get a speed of 112m/s using the data but there is something not correct about the data.
 
  • #5
Here is the problem in question. I can't seem to explain it without that picture of the string vibrator. on that worksheet i know that 8d is 4.41 N and 8e is 112 m/s. I know that 8f is 187 Hz but don't understand how to get that answer.
 

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  • #6
If I read it correctly a BALL of string 50m long has a mass of 0.0175kg.
The length of string vibrating is 1.2m (I think) from the diagram Diagram is not very clear
 
  • #7
That is my issue, I'm not sure whether 8f is referring to the diagram, or the previously gained data in the problem...
 
  • #8
Correct me if I'm wrong (which I think I am):

With the supposed answer of f = 187 Hz

and

v=f*λ

λ = 1/2 L

I get v = 112.2

This seems wildly incorrect but I can't see any fault in it.

Edit: Yeah turns out it was the diagram length that should have been used, it makes sense now.
 
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  • #9
if the string on the diagram is 1.2m long can you see that it is 2 wavelengths long?
If you know the wavelength and the speed then you can find frquency.
 
  • #10
After playing around with it. By using the aforementioned speed and the equation f=v/2L and using L=1.2. I find that 1.87. which is a few decimals off, but I think I'm close to it. v in that equation being equal to the square root of T/(m/L)
 
  • #11
Magical, that was the issue. It really was just that simple but with the diagram. Thank you!
 
  • #12
With 2 full wavelengths on the string, shouldn't λ = 1/2 L?
 
  • #13
if l = 1.2m and it is 2 wavelenths then wavelength = 0.6m
v = fλ 112 = f x 0.6 gives f = ??
this is all you need to do now
 
  • #14
for f=v/lamda I got the 187 Hz. Speed being 112, and with Wavelength being .6.
 
  • #15
Alright yeah so the issue was the length being confused in the diagram and the density calculation.
 
  • #16
Yes, i thought the length was the 50, but it was the 1.2 from the diagram.
 

What is the formula for calculating the frequency of a standing wave on a string?

The formula for calculating the frequency of a standing wave on a string is f = (n/2L) * v, where f is the frequency, n is the number of nodes, L is the length of the string, and v is the speed of the wave.

What factors affect the frequency of a standing wave on a string?

The frequency of a standing wave on a string is affected by the length of the string, the tension in the string, and the speed of the wave.

How does the number of nodes on a string affect the frequency of the standing wave?

The frequency of a standing wave on a string is directly proportional to the number of nodes on the string. This means that as the number of nodes increases, the frequency of the wave also increases.

What happens to the frequency of a standing wave on a string if the tension in the string is increased?

If the tension in the string is increased, the frequency of the standing wave also increases. This is because the speed of the wave is directly proportional to the tension in the string.

How does the frequency of a standing wave on a string change with the length of the string?

The frequency of a standing wave on a string is inversely proportional to the length of the string. This means that as the length of the string increases, the frequency of the wave decreases, and vice versa.

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