Question

A sound wave generated by a source of frequency 440 Hz is moving through 25 ^oC air. The sound wave strikes a solid block of steel and propagates into the steel. What is the wavelength of the sound wave inside the steel. The density of steel is 7.85 g/cm³ and the bulk modulus of steel is 1.6 x 10¹¹ N/m² . Select a choice

	1.	0.787 m
	2.	4515 m
	3.	346 m
	4.	10.26 m
	5.	1.27 m

Answer 1

Given that :

source of frequency, f = 440 Hz

density of steel, = 7.85 g/cm³ = 7850 kg/m³

bulk modulus of steel, B = 1.6 x 10¹¹ N/m²

using an equation, B = v²    { eq.1 }

or   v = B /

inserting the values in eq.1,

v = (1.6 x 10¹¹ N/m²) / (7850 kg/m³)

v = 0.0002038 x 10¹¹ m/s

v = 2.038 x 10⁷    m/s

v = 4514.4 m/s

and wavelength of the sound wave inside the steel will be given as ::

= v / f                                                                         { eq.2 }

inserting the values in eq.2,

= (4514.4 m/s) / (440 Hz)

= 10.26 m