Question

Source and observer start moving simultaneously along x and y-axis, respectively. The speed of source is twice the speed of observer, V₀. If the ratio of observed frequency to the frequency of the source is 0.75, find the velocity of sound.

• A. $\frac{11}{\sqrt{5}}{V}_0$
• B. $\frac{17}{\sqrt{5}}{V}_0$
• C. $\frac{16}{\sqrt{5}}{V}_0$
• D. $\frac{19}{\sqrt{5}}{V}_0$

Answer 1

The correct option is C $\frac{16}{\sqrt{5}}{V}_0$

$OS=2OPcos\alpha =\frac{2}{\sqrt{5}},cos\beta =\frac{1}{\sqrt{5}}{f}^{\prime }=f\left[\frac{V-V_{0}cos\beta }{V+V_{0}cos\beta }\right]=f\left[\frac{\frac{V-V_0}{\sqrt{5}}}{V+\left(2V_0\right)\times \left(\frac{2}{\sqrt{5}}\right)}\right]=f\left[\frac{\frac{V-V_0}{\sqrt{5}}}{\frac{V+4V_0}{\sqrt{5}}}\right]$

Given $\frac{f^{\prime }}{f}=\frac{3}{4}=\frac{V-x}{V+4x}1-\frac{3}{2}=\frac{5x}{V+4x}V=16x=\frac{16}{\sqrt{5}}{V}_0$