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Wave Motion and Waves on a String — Physics STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 SciencePhysicsWave Motion and Waves on a String2 Marks
Question
A pulse travelling on a string is represented by the function:

$\text{y}=\frac{\text{a}^3}{(\text{x}-\text{vt})^2+\text{a}^2},$

where a = 5mm and v = 20cm/s. Sketch the shape of the string at t = 0, 1s and 2s.Take x = 0 in the middle of the string.

✓

Answer

The pulse is given by, $ \text{y}=\Bigg[\frac{(\text{a}^3)}{\big\{(\text{x}-\text{vt})^2+\text{a}^2\big\}}\Bigg]$
a = 5mm = 0.5cm, v = 20cm/s
At t = 0s, $\text{y}=\frac{\text{a}^3}{(\text{x}^2+\text{a}^2)}$
The graph between y and x can be plotted by taking different values of x.
(left as exercise for the student)
Similarly, at t = 1s, $\text{y}=\frac{\text{a}^3}{\big\{(\text{x}-\text{v})^2+\text{a}^2\big\}}$
and at t = 2s, $\text{y}=\frac{\text{a}^3}{\big\{(\text{x}-2\text{v})^2+\text{a}^2\big\}}$

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