First slide

Standing waves

Question

In brass the velocity of longitudinal wave is 100 times the velocity of the transverse wave. If $Y = 1 \times 10^{11} N / m^{2}$ then stress in the wire is

Moderate

A

$1 \times 10^{13} N / m^{2}$
B

$1 \times 10^{9} N / m^{2}$
C

$1 \times 10^{11} N / m^{2}$
D

$1 \times 10^{7} N / m^{2}$

Solution

Velocity of longitudinal.l wave $= \sqrt{(Y / ρ)}$
where Y = Young's modulus and p = density of the material of wire.
Velocity of transverse wave $= \sqrt{(T / m)}$
where T = tension applied and m = mass per unit length
$∴ \frac{velocity of longitudinal wave}{velocity of transverse wave} = {[(\frac{Y}{ρ}) \times (\frac{{πr}^{2} ρ}{T})]}^{1 / 2} where r = radius of the wire = \sqrt{(\frac{{Yπr}^{2}}{T})} = \sqrt{(\frac{Y}{stress})} So, (100)^{2} = \frac{1 \times 10^{11}}{stress} or stress = \frac{(1 \times 10^{11})}{(10^{4})} = 1 \times 10^{7} N / m^{2}$

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