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If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is
- a)1 : 1
- b)√2 : 1
- c)1 : √2
- d)1 : 2
Correct answer is option 'C'. Can you explain this answer?
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If the initial tension on a stretched string is doubled, then the rat...
Given: Initial tension on a stretched string is doubled.
To find: The ratio of initial and final speeds of a transverse wave along the string.
Solution:
Let T be the initial tension in the string.
Let v be the initial speed of the wave along the string.
Using the formula v = √(T/μ), where μ is the linear density of the string, we can find the initial speed of the wave along the string.
Let v' be the final speed of the wave along the string when the tension is doubled.
Since the linear density of the string remains constant, we can write:
v' = √(2T/μ)
Taking the ratio of v' and v, we get:
v'/v = √(2T/μ) / √(T/μ)
v'/v = √(2T/μ) x √(μ/T)
v'/v = √(2T/T)
v'/v = √2
Therefore, the ratio of initial and final speeds of a transverse wave along the string is 1:√2 or √2:1.
The correct option is (C) 1:√2.
To find: The ratio of initial and final speeds of a transverse wave along the string.
Solution:
Let T be the initial tension in the string.
Let v be the initial speed of the wave along the string.
Using the formula v = √(T/μ), where μ is the linear density of the string, we can find the initial speed of the wave along the string.
Let v' be the final speed of the wave along the string when the tension is doubled.
Since the linear density of the string remains constant, we can write:
v' = √(2T/μ)
Taking the ratio of v' and v, we get:
v'/v = √(2T/μ) / √(T/μ)
v'/v = √(2T/μ) x √(μ/T)
v'/v = √(2T/T)
v'/v = √2
Therefore, the ratio of initial and final speeds of a transverse wave along the string is 1:√2 or √2:1.
The correct option is (C) 1:√2.
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If the initial tension on a stretched string is doubled, then the rat...
We know, velocity of transverse wave
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If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string isa)1 : 1b)√2 : 1c)1 : √2d)1 : 2Correct answer is option 'C'. Can you explain this answer?
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