Sound of single frequency travels from a medium into a medium

PHYSICS · Multi-part · CBSE · Physics · Waves · Waves

Problem

Sound of single frequency

\nu

travels from a medium

M_1

into a medium

M_2

. Let

v_1

and

v_2

be the respective speeds of sound in the two media. (a) Derive an expression for the ratio of the wavelengths

\lambda_2/\lambda_1

in the two media in terms of

v_1

and

v_2

. (b) Show that the fractional change in wavelength

(\lambda_2-\lambda_1)/\lambda_1

equals

(v_2-v_1)/v_1

. (c) Using your expression, calculate the percentage increase in wavelength when sound of frequency

600\,\text{Hz}

passes from air (

v_1 = 330\,\text{m/s}

) into sea water (

v_2 = 1500\,\text{m/s}

). (d) If the sound then enters a medium

M_3

where its speed is

990\,\text{m/s}

, determine whether the wavelength in

M_3

will be closer to its value in air or in water. Justify your answer quantitatively.