Consider a standing wave in a one dimensional ideal medium of length "d" (like a vibrating string).

a) how many vibration modes are possible with wavelengths between d/10 and d/20?

b) how many are possible with wavelengths between 10d and 20d?

a) 20 nodes    b) zero nodes

Explanation:

When we have standing waves in a bend we have nodes at the ends and the equation describes the number of possible waves in the string is

         L = n λ/2

Where λ is the wavelength, L is the length of the string, in our case it would be D and n is an entered. We can strip the wavelength of this expression

       λ = 2L / n

Let's calculate what value of n we have for a wavelength equal to D/10

       λ = 2D / n

       λ = D / 10

We match and calculate

       2D / n = D / 10

       2 / n = 1/10

       n = 20

Perform them for  λ = D / 20

       λ = 2D / n

       2D / n = D / 20

       n = 2 20 = 40

Since n is an inter there should be a wavelength for each value of n in the bone period there should be 20 different wavelengths

B) for La = 10D

       2D / n = 10D

       1 / n = 5

       n = 1/5 = 0.2

La = 20D

       2D / n = 20D

       1 / n = 10

      n = 1/10 = 0.1

These numbers are not entered so there can be no wave in this period

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