
Concept explainers
(a)
The wavelengths of fundemental and third harmonic before and after the addition of water.
(a)

Answer to Problem 50PQ
Value of fundamental wavelength with and without water will be the same and it is
Wavelength of third harmonic with and without water will be the same and it is
Explanation of Solution
Write the equation find the wavelength of first harmonic.
Here,
Note that there is no any term in the above equation which denotes the influence of medium which pipe is filled. It means that fundamental wavelength remain unchanged even the pipe is filled with water.
Write the equation find the wavelength of first harmonic.
Here,
The same explanation in the case of fundamental wavelength is applicable to this case also.. Wavelength of third harmonic remain unchanged even the pipe is filled with water.
Conclusion:
Substitute
Substitute
Therefore, value of fundamental wavelength with and without water will be the same and it is
Wavelength of third harmonic with and without water will be the same and it is
(b)
The frequencies of fundemental and third harmonic before and after the addition of water.
(b)

Answer to Problem 50PQ
Fundamental frequencies in air and water are
Third harmonic frequencies in air and water are
Explanation of Solution
Fundamental and third harmonic frequencies are function of speed of sound and it changes with medium. So, fundamental and third harmonic frequencies will be different in air and water.
Write the equation find the fundamental frequency in air.
Here,
Write the equation find the fundamental frequency in water.
Here,
Write the equation find the third harmonic frequency in air.
Here,
Write the equation find the third harmonic frequency in water.
Conclusion:
Substitute
Substitute
Substitute
Substitute
Therefore, fundamental frequencies in air and water are
Third harmonic frequencies in air and water are
(c)
Check whether lower pitched or high pitched sound will hear on tube is filled with water.
(c)

Answer to Problem 50PQ
High pitch sound will hear on tube is filled with water.
Explanation of Solution
Higher the pitch, higher will be the frequency of sound. Note that the frequency of sound when tube is filled with water is greater than that of tube filled with air. So the listener should hear higher pitch sound when the tube is filled with water.
Therefore, high pitch sound will hear on tube is filled with water.
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Chapter 18 Solutions
Physics for Scientists and Engineers: Foundations and Connections
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