Question

The greatest speed of transverse waves through a steel wire of radius 1 mm is ______ × 10² m. The breaking stress of steel is 6.0 × 10⁸ Nm^-2. Density of steel = 7800 kg m^-3.

Options

• 2.77

• 2.70

• 2.75

• 2.65

Answer 1

The greatest speed of transverse waves through a steel wire of radius 1 mm is 2.773 × 10² m. The breaking stress of steel is 6.0 × 10⁸ Nm^-2. Density of steel = 7800 kg m^-3.

Explanation:

Stress = `F/A`

Breaking stress = `F_{max}/A = 6 xx 10^8` Nm^-2

ρ = 7800 kg m^-3

Now, speed of transverse waves = `v = sqrt(T/mu)`

`v = sqrt(F/(m/l)) = sqrt(F/((Alrho)/l)) = sqrt(F/(Arho))`

`v_max = sqrt(F_max/(Arho)) = sqrt(((F_max)/A) 1/rho)`

= `sqrt((6 xx 10^8)/7800)`

= 2.773 × 10² m/s