Question

a string is vibrating in its fifth overtone between two rigid supports of 1.8m apart , what is the distance between successive nodes? please answer

Answer 1

Hey!


----> As the string is between two rigid supports which are 1.8m apart..

Hence, the wavelength of the string , can be considered as 1.8m

☞Now ,we know that the distance between the 2 successive nodes is one half of the wavelength .

Therefore, distance between two successive nodes is 1.8/2 = 0.9m ✓✓

Hope it helps... ^_^

Answer 2

Concept:

Half of the wavelength separates two subsequent nodes from one another. It is expressed as, d = λ/2

Given:

The separation between two rigid supports = 1.8m

The vibration of overtone = 5th

Find:

We need to determine the distance between the two successive nodes.

Solution:

A standing wave's node is the location along its length when its amplitude is at its smallest.

When there is the presence of the 5th overtone, there must be 6 loops and each loop should correspond to half the length of wavelength.

Therefore, the formula becomes,

6×λ/2 = L where L is the distance between two rigid supports, λ is the wavelength and 6 is the number of loops.

Therefore, L = 6 × λ/2

1.8 = 6 × λ/2

λ = (1.8 × 2) / 6

λ = 0.6m

We know, that the difference between two successive nodes is expressed as- d = λ/2

Therefore, d = 0.6/2

d = 0.3m

Thus, the distance between successive nodes is 0.3m.

#SPJ3