24 A string is fixed at one end and the other end is attached to a vibrator. The frequency of the
vibrator is slowly increased from zero. A series of stationary waves is formed. Assume that for a
stationary wave there is a node at point P.
string
Р
fixed
vibrator
L
What are the first five wavelengths of the stationary waves that could be formed?
A
211, 212, 213, 214, 215
212, 213, 214, 215, 2160
в 2
с
44
D
Answers
Answer:
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Concept:
Standing or Stationary waves are waves each having the same amplitude and frequency and the combination of two waves moving in opposite directions.
Wavelength can be represented as,
λ = 2L/n
where n is the number of wavelengths from first.
Given:
A stationary wave is formed when a string is fixed at one end and the other end is attached to a vibrator.
Find:
The first five wavelengths of the stationary waves formed.
Solution:
Wavelength can be represented as,
λ = 2L/n
where n is the number of wavelengths from first.
For the first wavelength, n = 1,
λ = 2L/1
Similarly, for the second wavelength, n = 2,
λ = 2L/2
Same, for n = 3, λ = 2L/3
n = 4, λ = 2L/4
n = 5, λ = 2L/5
Hence, the first five wavelengths of the stationary wave are 2L/1, 2L/2, 2L/3, 2L/4, and 2L/5. Hence, the correct option is (a) 2L/1, 2L/2, 2L/3, 2L/4, and 2L/5.
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