Question
Hard
Solving time: 5 mins
Q.182. Find the number of natural transverse vibrations of a string of length l in the frequency interval from ω to ω + dω if the propagation velocity of vibrations is equal to v. All vibrations are supposed to occur in one plane.
Text solutionVerified
Suppose the string is stretched along the axis from to with the end points fixed. Suppose is the transverse displacement of the element at at time t. Then obeys
We look for a stationary wave solution of this equation
where are constants.. In this from at . The further condition
implies
is the number of modes of frequency .
Thus
We look for a stationary wave solution of this equation
where are constants.. In this from at . The further condition
implies
is the number of modes of frequency .
Thus
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Question Text | Q.182. Find the number of natural transverse vibrations of a string of length l in the frequency interval from ω to ω + dω if the propagation velocity of vibrations is equal to v. All vibrations are supposed to occur in one plane. |
Topic | Nuclei |
Subject | Physics |
Class | Class 12 |
Answer Type | Text solution:1 |
Upvotes | 87 |