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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 String1 Mark
Question
Both the strings, shown in figure are made of same material and have same cross-section. The pulleys are light. The wave speed of a transverse wave in the string AB is $\nu_1$ and in CD it is $\nu_2.$ Then $\frac{\nu_1}{\nu_2}$ is:

  1. $1$

  2. $2$

  3. $\sqrt{2}$

  4. $\frac{1}{\sqrt{2}}.$

✓

Answer

  1. $\frac{1}{\sqrt{2}}$

Explanation:

TAB = T

TCD = 2T

where

TAB is the tension in the string AB

TCD is the tension in the stnng CD

The eelatlon between tension and the wave speed is given by

$\text{v}=\sqrt{\frac{\text{T}}{\mu}}$

$\text{v}\propto\sqrt{\text{T}}$

where

v is the wave speed of the transverse wave

$\mu$ is the mass per unit length of the string

$\frac{\text{v}_1}{\text{v}_2}=\sqrt{\frac{\text{T}}{2\text{T}}}$

$=\frac{1}{\sqrt{2}}$

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