In a certain alloy used for non-destructive testing

PHYSICS · Subjective · CBSE · Physics · Waves · Waves

Problem

In a certain alloy used for non-destructive testing, the speed of longitudinal ultrasonic waves shows mild dispersion and varies with frequency according to v(f)=v0(1+αf),v(f)=v_0\bigl(1+\alpha f\bigr), where v0=5000 m s−1v_0=5000\,\text{m\,s}^{-1}, α=2.0×10−8 s\alpha =2.0\times10^{-8}\,\text{s}, and ff is the frequency in hertz. (i) Derive an explicit expression for the wavelength λ(f)\lambda(f) of ultrasound propagating in the alloy as a function of frequency. (ii) Using your expression, calculate the speed and wavelength at (a) 1 MHz1\,\text{MHz} and (b) 10 MHz10\,\text{MHz}. (iii) Find the percentage change in wavelength when the frequency is increased from 1 MHz1\,\text{MHz} to 10 MHz10\,\text{MHz}. (iv) Briefly discuss how such frequency-dependent variation in wavelength could influence the achievable spatial resolution in high-frequency ultrasonic inspection of the alloy.

Related theory

Browse the problem library