Chapter 2: Q35E (page 499)

Interference of Rectangular Pulses. Figure E15.35 shows two rectangular wave pulses on a stretched string traveling toward each other. Each pulse is traveling with a speed of \(1.00\;{{{\rm{mm}}} \mathord{\left/ {\vphantom {{{\rm{mm}}} {\rm{s}}}} \right. \\} {\rm{s}}}\) and has the height and width shown in the figure. If the leading edges of the pulses are \(8.00\;{\rm{mm}}\) apart at \(t = 0\), sketch the shape of the string at \(t = 4.00\;{\rm{s}}\), \(t = 6.00\;{\rm{s}}\), and \(t = 10.0\;{\rm{s}}\).

Short Answer

Expert verified

The sketches are shown below.

Step by step solution

Identification of the given data

The given data can be listed below as,

The speed of pulses is, \(1.00\;{{{\rm{mm}}} \mathord{\left/ {\vphantom {{{\rm{mm}}} {\rm{s}}}} \right. \\} {\rm{s}}}\).
The given time is, \(t = 4.00\;{\rm{s}},\,t = 6.00\;{\rm{s}},\,t = 10.0\;{\rm{s}}\).

Significance of the principle of superposition

The consequences are vectorially additive if they are proportional to the causes and two or more physical causes are vectorially additive.

Determination of the shape of the string at \(t = 4.00\;{\rm{s}},\,t = 6.00\;{\rm{s}},\,t = 10.0\;{\rm{s}}\)

Once they have completely passed through one another, the pulses regain their initial shape after interfering with one another while they are in motion.

The figure below shows the string's shape at each designated period,