
Physics
1st Edition
ISBN: 9780133256925
Table of contents
Textbook solutions
All Solutions
Page 477: Practice Problems
Exercise 45
Solution 1
Solution 2
Step 1
1 of 3
$textbf{(a)}$ The given two waves are having the same phase. Therefore, the resultant wave will have the amplitude as addition of amplitudes of two given waves.
$$
begin{align*}
A_{res} & = A_1 + A_2
end{align*}
$$
The resultant is shown in the given figure.
Step 2
2 of 3
$textbf{(b)}$ The given two waves are having the opposite phase. Let us assume that both the waves have same amplitude. Therefore, the resultant wave will have zero amplitude. waves.
$$
begin{align*}
A_{res} & = A – A = 0
end{align*}
$$
The resultant is shown in the given figure.
Result
3 of 3
The addition of waves are shown in the given figures.
Step 1
1 of 1
In a) the amplitude increases to twice of its initial.
In b) the amplitude falls to zero
(these cases are true only if amplitude in both the graphs are equal)
Exercise 46
Step 1
1 of 6
The speed of the first wave and the second wave is given as
$$
begin{align*}
v_1 & = 1.0 mathrm{m/s} \
v_2 & = -1.0 mathrm{m/s}
end{align*}
$$
As time passes the first wave move towards right and the second wave move towards left.
Therefore, the sketch of the resultant wave at $t=1.0$ s is shown in the given figure.
Step 2
2 of 6
The sketch of the resultant wave at $t=2.0$ s is shown in the given figure.
Step 3
3 of 6
The sketch of the resultant wave at $t=2.5$ s is shown in the given figure.
Step 4
4 of 6
The sketch of the resultant wave at $t=3.0$ s is shown in the given figure.
Step 5
5 of 6
The sketch of the resultant wave at $t=4.0$ s is shown in the given figure.
Result
6 of 6
The sketches of the resultant wave are shown in the given figures.
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