Concept explainers
(a)
To show:
The coefficient of the reflection and transmission is zero and
(a)
Explanation of Solution
Given:
Formula used:
Consider:
Mass per unit length for the first string is given as:
Mass per unit length for the second string is given as:
The coefficient of the reflection is given as:
The coefficient of the transmission is given as:
Calculation:
The speed of the pulse on the first string is calculated as:
The speed of the pulse on the second string is calculated as:
Divide the equation (1) by equation (2) as:
Now, the coefficient of the reflection is calculated as:
Now put the values of
Hence, the coefficient of reflection at
The coefficient of the transmission is given as:
Divide the numerator and denominator of the above equation by
Now the put the value of the ratio of
Now put the values of
The coefficient of the transmission at
(b)
To show:
The coefficient of the reflection and transmission is
(b)
Explanation of Solution
Given:
Formula used:
Consider:
Mass per unit length for the first string is given as:
Mass per unit length for the second string is given as:
The coefficient of the reflection is given as:
The coefficient of the transmission is given as:
Calculation:
The speed of the pulse on the first string is calculated as:
The speed of the pulse on the second string is calculated as:
Divide the equation (1) by equation (2) as:
But as per the given condition: if
Now, the coefficient of the reflection is calculated as:
The coefficient of the transmission is given as:
Divide the numerator and denominator of the above equation by
The coefficient of the reflection and transmission at
(c)
To show:
The coefficient of the reflection and transmission is
(c)
Explanation of Solution
Given:
Formula used:
Consider:
Mass per unit length for the first string is given as:
Mass per unit length for the second string is given as:
The coefficient of the reflection is given as:
The coefficient of the transmission is given as:
Calculation:
The speed of the pulse on the first string is calculated as:
The speed of the pulse on the second string is calculated as:
Divide the eq. (1) by eq. (2) as:
But as per the given condition: if
Now, the coefficient of the reflection is calculated as:
The coefficient of the transmission is given as:
Divide the numerator and denominator of the above equation by
The coefficient of the reflection and transmission at
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Chapter 15 Solutions
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