Solved Example Problems for Velocity of Waves in Different Media

EXAMPLE 11.6

Calculate the velocity of the travelling pulse as shown in the figure below. The linear mass density of pulse is 0.25 kg m-1. Further, compute the time taken by the travelling pulse to cover a distance of 30 cm on the string.

Solution

The tension in the string is T = m g = 1.2 × 9.8 = 11.76 N

The mass per unit length is μ = 0.25 kg m-1. Therefore, velocity of the wave pulse is

The time taken by the pulse to cover the distance of 30 cm is

where

ms = milli second.

Velocity of longitudinal waves in an elastic medium

EXAMPLE 11.7

Calculate the speed of sound in a steel rod whose Young’s modulus Y = 2 × 1011 N m-2 and ρ = 7800 kg m-3.

Solution

Therefore, longitudinal waves travel faster in a solid than in a liquid or a gas. Now you may understand why a shepherd checks before crossing railway track by keeping his ears on the rails to safegaurd his cattle.

EXAMPLE 11.8

An increase in pressure of 100 kPa causes a certain volume of water to decrease by 0.005% of its original volume.

(a) Calculate the bulk modulus of water?.

(b) Compute the speed of sound (compressional waves) in water?.

Solution

(a) Bulk modulus

(b) Speed of sound in water is