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A pipe open at both the ends produce a note of fundamental frequency v1. When the pipe is kept with (3/4)th of its length in water, it produces a note of fundamental frequency v2. The ratio of v1/v2 is
- a)4/3
- b)3/4
- c)2
- d)1/2
Correct answer is option 'D'. Can you explain this answer?
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Given:
A pipe open at both ends produces a note of fundamental frequency v1. When the pipe is kept with (3/4)th of its length in water, it produces a note of fundamental frequency v2.
To find: The ratio of v1/v2.
Solution:
Fundamental frequency of an open pipe of length L is given by v = (v/2L) where v is the speed of sound in air.
Let the length of the pipe be L.
Given:
Fundamental frequency of the pipe open at both ends is v1.
Fundamental frequency of the pipe with (3/4)th of its length in water is v2.
Length of the pipe open at both ends = L
Length of the pipe with (3/4)th of its length in water = L - (3/4)L = (1/4)L
Frequency of the pipe open at both ends is given by v1 = (v/2L)
Frequency of the pipe with (3/4)th of its length in water is given by v2 = (v/2(1/4)L) = 4(v/2L)
Therefore, the ratio of v1/v2 = (v/2L)/(4(v/2L)) = 1/4
Hence, the correct answer is option D, 1/2.
A pipe open at both ends produces a note of fundamental frequency v1. When the pipe is kept with (3/4)th of its length in water, it produces a note of fundamental frequency v2.
To find: The ratio of v1/v2.
Solution:
Fundamental frequency of an open pipe of length L is given by v = (v/2L) where v is the speed of sound in air.
Let the length of the pipe be L.
Given:
Fundamental frequency of the pipe open at both ends is v1.
Fundamental frequency of the pipe with (3/4)th of its length in water is v2.
Length of the pipe open at both ends = L
Length of the pipe with (3/4)th of its length in water = L - (3/4)L = (1/4)L
Frequency of the pipe open at both ends is given by v1 = (v/2L)
Frequency of the pipe with (3/4)th of its length in water is given by v2 = (v/2(1/4)L) = 4(v/2L)
Therefore, the ratio of v1/v2 = (v/2L)/(4(v/2L)) = 1/4
Hence, the correct answer is option D, 1/2.
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A pipe open at both the ends produce a note of fundamental frequency v1.When the pipe is kept with (3/4)thof its length in water, it produces a note offundamental frequency v2.The ratio of v1/v2isa)4/3b)3/4c)2d)1/2Correct answer is option 'D'. Can you explain this answer?
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