9. Consider rigid rod of Young's modulus \( Y \), its density varies according to \( \rho=\rho_{0}(1+k x) \) from the end shown in figure. Area of cross section of the rod remain constant along its lengths. If amplitude of vibrator performing SHM is \( A_{0} \) and frequency is \( f_{0} \) respectively, then : (Assume amplitude of SHM of vibrator is small and rod remains stationary) (A) Amplitude of a point at a distance \( x \) from end is \( \frac{A_{0}}{\sqrt{1+K x}} \) (B) Wave length of wave motion as a function \( x \) is given by, \( \lambda=\frac{1}{f_{0}} \sqrt{\frac{Y}{(1+K x) \rho_{0}}} \) (C) time taken by pulse to reach at a distance \( \times \frac{2}{3} \sqrt{\left(\frac{1+K x}{K^{2}}\right)^{3} \frac{\rho_{0}}{Y}} \) is (D) frequency of wave throught rod independent of

Question

9. Consider rigid rod of Young's modulus \( Y \), its density varies according to \( \rho=\rho_{0}(1+k x) \) from the end shown in figure. Area of cross section of the rod remain constant along its lengths. If amplitude of vibrator performing SHM is \( A_{0} \) and frequency is \( f_{0} \) respectively, then : (Assume amplitude of SHM of vibrator is small and rod remains stationary) (A) Amplitude of a point at a distance \( x \) from end is \( \frac{A_{0}}{\sqrt{1+K x}} \) (B) Wave length of wave motion as a function \( x \) is given by, \( \lambda=\frac{1}{f_{0}} \sqrt{\frac{Y}{(1+K x) \rho_{0}}} \) (C) time taken by pulse to reach at a distance \( \times \frac{2}{3} \sqrt{\left(\frac{1+K x}{K^{2}}\right)^{3} \frac{\rho_{0}}{Y}} \) is (D) frequency of wave throught rod independent of \( x \)