Question

A violin string of length L is fixed at both ends. Which one of these is not a wavelength of a standing wave on the string? A) L/2 B) L/3 C) 2L/3 D) 3L/2​

Answer 1

Answer:

i think option d is the correct answer

Answer 2

Answer:

The correct answer will be

(D) 3L/2

Explanation:

Given,

A Violin string of length L is fixed at both ends.

• The number of antinodes will be = the harmonic number of that pattern.
• So the wavelength of the nth Harmonic has n antinodes where n is an integer which represents the harmonic number.

So for the nth harmonic wavelength will be -

$L = \frac{n}{2} \lambda$

so in the same way the wavelength will also be given by -

$\lambda = \frac{2}{n}L$

Now check all the options -

For n = 1, $\lambda = \frac{2}{1}L = 2L$

For n = 2, $\lambda = \frac{2}{2}L = L$

For n = 3, $\lambda = \frac{2}{3}L$

For n = 4, $\lambda = \frac{2}{4}L = \frac{1}{2} L$

For n = 6, $\lambda = \frac{2}{6}L = \frac{1}{3} L$

We got all the options except option (D) 3L/2

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