Question

Physics genius help me..... a 4m long string fixed at its ends resonate in 4 segments to wavelenghth of the wave is​

Answer 1

calculate the wavelength of a standing wave

 Either by using the distance between adjacent nodes/antinodes or by using the wave speed equation.

These two methods can only be used if you know the relevant data.

Method 1

If you know the distance between nodes and antinodes, or if you know the length of string (or pipe length) and which harmonic is present.

If you know the distance between nodes and antinodes then use this equation:

λ \ 2 =D

Where D is the distance between adjacent nodes or antinodes.

If you know the harmonic and length of string then you need to relate the wavelength to the length of string/pipe (L) using the following:

For strings and open pipes

Harmonic, Wavelength in terms of L

1,  λ/2

2,  λ \ 3,

3,λ/2  

4,  2\λ

Etc. Notice amount of wavelength present increases by half each time.

For closed pipes

Harmonic, Wavelength in terms of L

1,  λ/4\

 2,  3λ/4  

3,  5λ/4

4,  7λ/4

Etc. Notice amount of wavelength present increases by half each time.

Method 2

If you know the frequency and wave speed of the progressive waves that made the standing wave you can use the following equation:

λ

= c  \ f

I hope this was helpful to you......