Question

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?

Answer 1

a) 20 nodes b) zero nodes

Step-by-step 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