Chapter 18, Problem 18.2P

Two wave pulses A and B are moving in opposite directions, each with a speed v = 2.00 cm/s. The amplitude of A is twice the amplitude of B. The pulses are shown in Figure P17.3 at t = 0. Sketch the resultant wave at t = 1.00 s, 1.50 s, 2.00 s, 2.50 s, and 3.00 s.

Figure P17.3

To determine

To sketch: The graph of the resultant wave at different time period.

Explanation of Solution

Introduction: Wave is a disturbance that transfers the energy from one place two other through a matter and the amplitude denotes the intensity of the wave.

Section 1:

To sketch: The graph of the resultant wave at time $t=1\text{s}$.

Introduction: Wave is a disturbance that transfers the energy from one place two other through a matter and the amplitude denotes the intensity of the wave.

Explanation:

Given information: The speed of the waves $A$ and $B$ is $2\text{cm}/\text{s}$ and the amplitude of the wave $A$ is twice than the amplitude of the wave $B$.

The given Figure of the pluses is shown below.

Figure (I)

Formula to calculate distance is,

$d=vt$

• $d$ is the distance
• $v$ is the speed of the wave.
• $t$ is the time travel of two in opposite direction to each other.

Substitute $2\text{cm}/\text{s}$ for $v$ and $1\text{s}$ for $t$.

$\begin{array}{c}d=\left(2\text{cm}/\text{s}\right)\left(1\text{s}\right)\\ =2\text{cm}\end{array}$

The two waves $A$ and $B$ will move towards each other by the distance of $2\text{cm}$ along $x$ axis.

Thus, the graph of the resultant wave at $t=1\text{s}$ is shown below.

Figure (II)

Conclusion:

Therefore, the graph of the resultant wave at time $t=1\text{s}$ is shown in Figure (II).

Section 2:

To sketch: The graph of the resultant wave at time $t=1.5\text{s}$.

Introduction: Wave is a disturbance that transfers the energy from one place two other through a matter and the amplitude denotes the intensity of the wave.

Explanation:

Given information: The speed of the waves $A$ and $B$ is $2\text{cm}/\text{s}$ and the amplitude of the wave $A$ is twice than the intensity of the wave $B$.

At $t=1.5\text{s}$,

Formula to calculate distance at  is,

$d=vt$

• $d$ is the distance
• $v$ is the speed of the wave.
• $t$ is the time travel of two in opposite direction to each other.

Substitute $2\text{cm}/\text{s}$ for $v$ and $1.5\text{s}$ for $t$.

$\begin{array}{c}d=\left(2\text{cm}/\text{s}\right)\left(1.5\text{s}\right)\\ =3\text{cm}\end{array}$

The two waves $A$ and $B$ will move towards each by $3\text{cm}$ along $x$ axis.

Thus, the graph of the resultant wave at $t=1.5\text{s}$ is shown below.

Figure (III)

Conclusion:

Therefore, the graph of the resultant wave is at time $t=1.5\text{s}$ is shown in Figure (III).

Section 3:

To sketch: The graph of the resultant wave at time $t=2\text{s}$.

Introduction: Wave is a disturbance that transfers the energy from one place two other through a matter and the amplitude denotes the intensity of the wave.

Explanation:

Given information: The speed of the waves $A$ and $B$ is $2\text{cm}/\text{s}$ and the amplitude of the wave $A$ is twice than the intensity of the wave $B$.

Formula to calculate distance at  is,

$d=vt$

• $d$ is the distance
• $v$ is the speed of the wave.
• $t$ is the time travel of two in opposite direction to each other.

Substitute $2\text{cm}/\text{s}$ for $v$ and $2\text{s}$ for $t$.

$\begin{array}{c}d=\left(2\text{cm}/\text{s}\right)\left(2\text{s}\right)\\ =4\text{cm}\end{array}$

The two waves $A$ and $B$ will move towards each by $4\text{cm}$ along $x$ axis.

Thus, the graph of the resultant wave at $t=2\text{s}$ is shown below.

Figure (IV)

Conclusion:

Therefore, the graph of the resultant wave at time $t=2\text{s}$ is shown in Figure (IV).

Section 4:

To sketch: The graph of the resultant wave at time $t=2.5\text{s}$.

Introduction: Wave is a disturbance that transfers the energy from one place two other through a matter and the amplitude denotes the intensity of the wave.

Explanation:

Given information: The speed of the waves $A$ and $B$ is $2\text{cm}/\text{s}$ and the amplitude of the wave $A$ is twice than the intensity of the wave $B$.

Formula to calculate distance at  is,

$d=vt$

• $d$ is the distance
• $v$ is the speed of the wave.
• $t$ is the time travel of two in opposite direction to each other.

Substitute $2\text{cm}/\text{s}$ for $v$ and $2.5\text{s}$ for $t$.

$\begin{array}{c}d=\left(2\text{cm}/\text{s}\right)\left(2.5\text{s}\right)\\ =5\text{cm}\end{array}$

The two waves $A$ and $B$ will move towards each by $5\text{cm}$ along $x$ axis.

Thus, the graph of the resultant wave at $t=2.5\text{s}$ is shown below.

Figure (V)

Conclusion:

Therefore, the graph of the resultant wave is at time $t=2.5\text{s}$ is shown in Figure (V).

Section 5:

To sketch: The graph of the resultant wave at time $t=3\text{s}$.

Introduction: Wave is a disturbance that transfers the energy from one place two other through a matter and the amplitude denotes the intensity of the wave.

Explanation:

Given information: The speed of the waves $A$ and $B$ is $2\text{cm}/\text{s}$ and the amplitude of the wave $A$ is twice than the intensity of the wave $B$.

Formula to calculate distance at  is,

$d=vt$

• $d$ is the distance
• $v$ is the speed of the wave.
• $t$ is the time travel of two in opposite direction to each other.

Substitute $2\text{cm}/\text{s}$ for $v$ and $3\text{s}$ for $t$.

$\begin{array}{c}d=\left(2\text{cm}/\text{s}\right)\left(3\text{s}\right)\\ =6\text{cm}\end{array}$

The two waves $A$ and $B$ will move towards each by $6\text{cm}$ along $x$ axis.

Thus, the graph of the resultant wave at $t=3\text{s}$ is shown below.

Figure (VI)

Conclusion:

Therefore, the graph of the resultant wave is at time $t=3\text{s}$ is shown in Figure (VI).