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The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d?
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The frequency of the fundamental mode of transverse vibration of stret...
Explanation:
When a wire is stretched and fixed at both ends, it vibrates transversely in its fundamental mode with a certain frequency. The frequency of vibration depends on the length, tension, and mass per unit length of the wire.
Given:
Length of wire, l1 = 1000mm
Frequency of fundamental mode, f1 = 200Hz
Shortened length of wire, l2 = 500mm
Frequency of fundamental mode when shortened, f2 = ?
Solution:
Relation between frequency and length:
The frequency of the fundamental mode of vibration of a wire is inversely proportional to its length when the tension and mass per unit length are constant. i.e. f ∝ 1/l
Relation between frequency and tension:
The frequency of the fundamental mode of vibration of a wire is directly proportional to the square root of its tension when the length and mass per unit length are constant. i.e. f ∝ √T
Relation between frequency and mass per unit length:
The frequency of the fundamental mode of vibration of a wire is inversely proportional to the square root of its mass per unit length when the length and tension are constant. i.e. f ∝ 1/√m
Using the above relations:
For the initial length of the wire:
f1 ∝ 1/l1
For the shortened length of the wire:
f2 ∝ 1/l2
Since the tension is constant, we can equate the two relations:
f1/f2 = l2/l1
Substituting the given values, we get:
200/f2 = 500/1000
f2 = 400Hz
Therefore, the fundamental frequency of transverse vibration of the wire when shortened to 500mm at the same tension is 400Hz.
Answer:
Option d) 400Hz.
When a wire is stretched and fixed at both ends, it vibrates transversely in its fundamental mode with a certain frequency. The frequency of vibration depends on the length, tension, and mass per unit length of the wire.
Given:
Length of wire, l1 = 1000mm
Frequency of fundamental mode, f1 = 200Hz
Shortened length of wire, l2 = 500mm
Frequency of fundamental mode when shortened, f2 = ?
Solution:
Relation between frequency and length:
The frequency of the fundamental mode of vibration of a wire is inversely proportional to its length when the tension and mass per unit length are constant. i.e. f ∝ 1/l
Relation between frequency and tension:
The frequency of the fundamental mode of vibration of a wire is directly proportional to the square root of its tension when the length and mass per unit length are constant. i.e. f ∝ √T
Relation between frequency and mass per unit length:
The frequency of the fundamental mode of vibration of a wire is inversely proportional to the square root of its mass per unit length when the length and tension are constant. i.e. f ∝ 1/√m
Using the above relations:
For the initial length of the wire:
f1 ∝ 1/l1
For the shortened length of the wire:
f2 ∝ 1/l2
Since the tension is constant, we can equate the two relations:
f1/f2 = l2/l1
Substituting the given values, we get:
200/f2 = 500/1000
f2 = 400Hz
Therefore, the fundamental frequency of transverse vibration of the wire when shortened to 500mm at the same tension is 400Hz.
Answer:
Option d) 400Hz.
Community Answer
The frequency of the fundamental mode of transverse vibration of stret...
Frequency (n) =1/2L under root T/m so from This N1L1=N2L2 so 200*1000=N2*500 so from this N2=400Hz
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The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d?
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The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d?.
The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The frequency of the fundamental mode of transverse vibration of stretched wire 1000mm long is 200hz when the wire is shortened to 500mm at the same tension. What is the fundamental frequency a)100hz b)150hz c)200hz d)400hz .correct option is d?.
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