Solving Wave Propagation Dilemma: Length Increase of 10%

In summary, a wave takes 4s to travel from one end of the string to the other. 10% more length equals a wave that takes 5s to travel the same distance.
  • #1
dimpledur
194
0

Homework Statement



A wave takes 4s to travel form one end of the string to the other. Then the length is increased by 10%. Now how long does a wave take to travel the length of the spring?

Homework Equations



v = sqrt ( FL/m)
F = -kx

The Attempt at a Solution



If the original stretch was x, then an increase of ten percent would be:
1.1x.

So, if F = -kx, and since k is constant, if x increases by a factor of 1.1, then as does F. SO the tensional force is 1.1F the original.

v = sqrt ( 1.1F*L/m)
(delta d) / (delta t) = sqrt ( 1.1F*L/m)
taking the inverse:
(delta t) / (delta d) = sqrt ( m/1.1F*L)

where (delta d = 1.1L) since it has increased by ten percent.

So,

delta t = 1.1L*sqrt ( m/1.1F*L)
so the original delta t must increase by a factor of 1.1/sqrt(1.1)

?

?
 
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  • #2
So, if F = -kx, and since k is constant, if x increases by a factor of 1.1, then as does F.
I don't understand this. The question doesn't say anything about the force or tension changing. Making the string longer might DEcrease the force but it sure wouldn't increase it.
 
  • #3
It's actually a spring, but I was under the impression if you stretched a spring, you increased the tension..
 
  • #4
Oh, sorry - I was thinking of putting a longer string on a guitar!

Using "v = sqrt ( FL/m)", it would appear that F increases by 1.1 and L increases by 1.1.
So the new v is 1.1 times the old v.
 
  • #5
I was under the impression that L/m was a constant, regardless of whether it was stretched, since m/L is the linear mass density.
 
  • #6
so L is the length? If so, L increases by a factor of 1.1, doesn't it?
The mass per unit length would decrease when the length increases.
 
  • #7
I came here because apparently the velocity does not change.. I don't get how it doesn't change, though/
 
  • #8
Oh, that's the answer I got! Using L increases by a factor of 1.1 and v increases by a factor of 1.1 in the formula t = d/v.
 
  • #9
lol ill check it out thanks
 

Related to Solving Wave Propagation Dilemma: Length Increase of 10%

1. How does the length increase of 10% affect wave propagation?

The length increase of 10% can affect wave propagation in several ways. It can cause a change in the wavelength and frequency of the wave, which can alter its speed and direction. Additionally, it may also lead to interference or diffraction, depending on the type of wave.

2. What factors contribute to the length increase of 10% in wave propagation?

The length increase of 10% in wave propagation can be caused by various factors such as changes in the medium through which the wave is traveling, changes in the source of the wave, or changes in the properties of the wave itself. It can also be affected by external factors such as temperature, pressure, or humidity.

3. How can the length increase of 10% be measured or calculated?

The length increase of 10% can be measured using various methods depending on the type of wave. For electromagnetic waves, it can be measured using a ruler or measuring instrument. For sound waves, it can be measured using a microphone and an oscilloscope. It can also be calculated using mathematical formulas that take into account the wavelength and frequency of the wave.

4. What are the potential consequences of a length increase of 10% in wave propagation?

The consequences of a length increase of 10% in wave propagation can vary depending on the situation. In some cases, it may cause a distortion or disruption in the wave, leading to a decrease in its intensity or energy. It can also result in a change in the perceived pitch or frequency of the wave. In certain scenarios, it may have a negligible effect on the wave and may go unnoticed.

5. How can the length increase of 10% be mitigated or controlled in wave propagation?

The length increase of 10% in wave propagation can be mitigated or controlled by altering the properties of the medium through which the wave is traveling. For example, changing the temperature or pressure of the medium can affect the speed of the wave and, in turn, its length. Additionally, adjusting the source of the wave or using specialized materials can also help in controlling the length increase of 10% in wave propagation.

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