Standing Waves Question: Find Wavelength and Amplitude in Two Connected Strings

In summary, the conversation discusses a problem involving two strings with different linear mass densities connected by constant tension. The first string has a wave with amplitude of 10 cm and wavelength of 10 cm. The goal is to find the wavelength and amplitude of the wave in the second string, assuming constant frequency. The first part is solved by noticing that the velocity in the second string is a factor of √2/2 smaller than the first, resulting in a wavelength of 7 cm. The second part is harder to solve, but the conversation mentions a formula for finding the amplitude and suggests calculating it using the values for k= 2π/λ.
  • #1
Just_some_guy
16
0
This is my first post on the forum, and I hope you guys can help me

My questions is this,
There are two strings which are connected with constant tension everywhere, but they have different linear mass densities. The second mass density is double that of the first (μ1= 2μ1). A wave propagates along the "lighter" string with an amplitude of 10 cm and a wavelength of 10 cm. I have to find the wavelength of the wave propagated through the second string, assuming frequency is the same everywhere, and also what is the amplitude of the transmitted wAve?

Relevant equations which I have used are

v= ω/k = λω/2π where k= 2π/λ

Also v^2 = T/μ

All I have done so far is to notice that if the second mass density is double the first then the second velocity is a factor of sqrt2/2 smaller than the first? So would λ then simply be the same factor larger than that of the first wavelength as frequency is constant?If this is the case then my answer was 14 cm

I haven't yet begun the second part as I wanted to do the first part firstCheers!
 
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  • #2
I hope my question is clear
 
Last edited:
  • #3
Ok I have now calculated a value for lambda 2I got 14 cmUsing v1/λ1= v2/λ2

And put v1= sqrt2 / 2 and v2= 1 because that's the factor between the two as tension is uniform and frequency is equal over all parts
 
Last edited:
  • #4
I think your ratio between the speeds is upside down. Since the wave passes from the lighter spring to the heavier one, the wave slows down and shrinks by a factor of √2. Besides this minor mistake, the procedure you used is correct. The second question is harder to solve.
 
  • #5
So my new wavelength would then be

7 cm rather than 14, by getting rid of my factor of 1/2Do you have any suggestions for the second part I'm not so sure?:(
 
  • #6
Would the answer not have to be 14 cm

As v= fλ then if we have velocity decreasing then to compensate and keep frequency the same then wavelength must surely increase? Not decrease also?
 
  • #7
Just_some_guy said:
Would the answer not have to be 14 cm

As v= fλ then if we have velocity decreasing then to compensate and keep frequency the same then wavelength must surely increase? Not decrease also?

You're confused. If the left side of the equation decreases than the right side must ALSO DECREASE to compensate.
 
  • #8
So 7 cm would be the correct answer
 
  • #9
Just_some_guy said:
So 7 cm would be the correct answer

So it seems.
 
  • #10
That makes sense, I was mixing up the formula I was using:(
Anyways thanks, I also found I good way to find amplitude...

A2/A1 = 2k1/ k1+ k2

And calculated each term according to k= 2π/λ
 

1. What is a standing wave?

A standing wave is a type of wave that forms when two waves with the same wavelength and amplitude travel in opposite directions and interfere with each other. This creates nodes, points of no movement, and antinodes, points of maximum movement, along the wave.

2. How are standing waves formed?

Standing waves are formed when two waves with the same frequency and amplitude travel in opposite directions and superimpose, or overlap, with each other. This causes the waves to interfere and create nodes and antinodes.

3. What is the difference between a standing wave and a traveling wave?

A standing wave stays in one place and does not transfer energy, whereas a traveling wave moves through space and transfers energy. A standing wave is formed by the interference of two waves, while a traveling wave is created by a disturbance or source.

4. What are some real-life examples of standing waves?

Some common examples of standing waves include musical instruments such as guitar strings, organ pipes, and drums. Other examples include microwave ovens, which use standing waves to heat food, and earthquake waves that can form standing waves in buildings and bridges.

5. How are standing waves used in science and technology?

Standing waves have various applications in science and technology. They are used in musical instruments to produce specific frequencies and harmonics. They are also used in medical imaging techniques such as ultrasound and in telecommunications for signal transmission. Additionally, standing waves are studied in physics to better understand wave properties and principles of interference and resonance.

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