For water at

PHYSICS · Subjective · CBSE · Physics · Waves · Waves

Problem

For water at

20^{\circ}\text{C}

, the speed of sound varies slightly with frequency according to

v(f)=v_0\bigl(1+0.0001\,f_{\text{MHz}}\bigr)

, where

v_0=1480\,\text{m\,s}^{-1}

and

f_{\text{MHz}}

is the frequency in megahertz. (i) Find the wavelength of ultrasound at

10\,\text{MHz}

. (ii) Find the wavelength at

30\,\text{MHz}

. (iii) Hence compute the ratio of the two wavelengths and comment briefly on whether this slight dispersion is likely to affect imaging quality.