Alex3543
contestada

Which of the following wavelengths will produce standing waves on a string that is 3.5 m long?

A. 1.75m
B. 3.5m
C. 5m
D. 7m

Respuesta :

skyluke89

In a string of length L, the wavelength of the n-th harmonic of the standing wave produced in the string is given by:

[tex] \lambda=\frac{2}{n} L [/tex]


The length of the string in this problem is L=3.5 m, therefore the wavelength of the 1st harmonic of the standing wave is:

[tex] \lambda=\frac{2}{1} \cdot 3.5 m=7.0 m[/tex]


The wavelength of the 2nd harmonic is:

[tex] \lambda=\frac{2}{2} \cdot 3.5 m=3.5 m[/tex]


The wavelength of the 4th harmonic is:

[tex] \lambda=\frac{2}{4} \cdot 3.5 m=1.75 m[/tex]


It is not possible to find any integer n such that [tex] \lambda=5 m [/tex], therefore the correct options are A, B and D.

ajeigbeibraheem

The correct option from the following wavelength is A, B, and D.

What is the nth term of a harmonic wavelength?

In simple harmonic wavelength, the length of string L and the wavelength of the nth harmonic wave produced in the string can be expressed by using the formula:

[tex]\mathbf{\lambda = \dfrac{2}{n}L}[/tex]

where;

  • λ = wavelength
  • L = length

Given that, the length of the string L = 3.5

Then, the wavelength of the first harmonic of the standing wave is:

[tex]\mathbf{\lambda = \dfrac{2}{1}\times 3.5}[/tex]

λ = 7.0 cm

The wavelength of the second harmonic of the standing wave is:

[tex]\mathbf{\lambda = \dfrac{2}{2}\times 3.5}[/tex]

λ = 3.5 cm

The wavelength of the fourth harmonic of the standing wave is:

[tex]\mathbf{\lambda = \dfrac{2}{4}\times 3.5}[/tex]

λ = 1.75 cm



Learn more about wavelength here:

https://brainly.com/question/10728818

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