Question

23.
The wave length of 2m long string having 3 loops, is in meter
A.1
C.1.50
B.1.55
D.1.333
With solutiin please

Answer 1

Answer:

As discussed in Lesson 4, standing wave patterns are wave patterns produced in a medium when two waves of identical frequencies interfere in such a manner to produce points along the medium that always appear to be standing still. Such standing wave patterns are produced within the medium when it is vibrated at certain frequencies. Each frequency is associated with a different standing wave pattern. These frequencies and their associated wave patterns are referred to as harmonics. A careful study of the standing wave patterns reveal a clear mathematical relationship between the wavelength of the wave that produces the pattern and the length of the medium in which the pattern is displayed. Furthermore, there is a predictability about this mathematical relationship that allows one to generalize and deduce a statement concerning this relationship. To illustrate, consider the first harmonic standing wave pattern for a vibrating rope as shown below.

Analyzing the First Harmonic Pattern

The pattern for the first harmonic reveals a single antinode in the middle of the rope. This antinode position along the rope vibrates up and down from a maximum upward displacement from rest to a maximum downward displacement as shown. The vibration of the rope in this manner creates the appearance of a loop within the string. A complete wave in a pattern could be described as starting at the rest position, rising upward to a peak displacement, returning back down to a rest position, then descending to a peak downward displacement and finally returning back to the rest position. The animation below depicts this familiar pattern. As shown in the animation, one complete wave in a standing wave pattern consists of two loops. Thus, one loop is equivalent to one-half of a wavelength.

In comparing the standing wave pattern for the first harmonic with its single loop to the diagram of a complete wave, it is evident that there is only one-half of a wave stretching across the length of the string. That is, the length of the string is equal to one-half the length of a wave. Put in the form of an equation:

Answer 2

The correct answer is option (d). 1.333.

Given:

The length of the string = 2m.

The number of loops in the string = 3.

To Find:

We have to find the wave length (λ) of a 2m long string having 3 loops, in meter.

Solution:

Given that the 2m long string have 3 loops in it.

The length of one loop = The length of the string ÷ Number of loops in the string.

Substituting the given values, the above equation becomes,

The length of one loop = $\frac{2}{3} = 0.666666667$ m.

∴, The length of 2 loops = $0.666666667$ × $2 = 1.333$ m.

The length of two loops constitute the wavelength of the given string.

∴, The wavelength of the string, λ = The length of 2 loops $= 1.333$ m.

Hence, the wave length of a 2m long string having 3 loops is 1.333 meter.

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