Concept explainers
(a)
Find the depth of the well.
(a)
Answer to Problem 53P
The depth of the well is
Explanation of Solution
Here, the well acts like a pipe open at one end and closed at the other end. The normal mode of vibration of the pipe is odd harmonics.
Write the expression for depth of the well.
Here,
Write the relation between frequency, wavelength and speed.
Here,
Write the relation between frequency, wavelength and speed at next instant resonance.
Here,
The expression for the next resonance instant, depth of the well is,
Conclusion:
Substitute equation (II) in equation (I).
Substitute equation (III) in equation (IV).
Solve the equation (V) and (VI).
Substitute
Solve the above equation for
Substitute
Therefore, the depth of the well is
(b)
The number of antinodes are formed in standing wave at frequency
(b)
Answer to Problem 53P
The number of 7 antinodes are formed in standing wave at frequency
Explanation of Solution
Write the expression for fundamental frequency for first harmonic.
Here,
Write the expression to calculate the number of harmonics.
Here,
Conclusion:
Substitute
The pattern for above frequency is AN, similarly the 3rd harmonic pattern is ANAN, and the 5th harmonic is ANANAN etc.
Substitute
The pattern with number of antinodes is calculated as,
Rewrite the above relation for
Substitute 13 for
Therefore, the number of 7 antinodes are formed in standing wave at frequency
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Chapter 18 Solutions
Physics for Scientists and Engineers With Modern Physics
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