1905 words - 8 pages

An experiment to find the acoustic impedance of paraffin and water

Abstract

The speed of sound through paraffin and water was measured, and came close to the generally expected value. The speed in was calculated as 1458.36±16.2ms^(-1) in water and 1212±23.7ms^(-1) in paraffin. Then the density of these two liquids was measured, and combined with the speed of sound to find the acoustic impedance. . The acoustic impedance of water was 1575±29kgm^(-2) s^(-1) and the acoustic impedance of paraffin was 1066.6±32kgm^(-2) s^(-1) . To check that these values were correct the reflection coefficient of a boundary between paraffin and water was calculated using the acoustic impedances of the liquid, then found by comparing the amplitudes of the transmitted and reflected waves. The values were 0.192±0.02 and 0.13±0.02, which are close enough to each other to validate that the acoustic impedances measured are quite accurate.

introduction

When a wave travelling through a material hits a boundary with another material it is affected by the boundary and some of it will be reflected back. How much is reflected back depends on the acoustic impedance of the materials at the boundary.

This experiment will find, experimentally, the acoustic impedance of paraffin and water. This will be done by measuring the density of these materials and the speed of sound through them. The values obtained for the acoustic impedance will be used to find the reflection coefficient of the boundary. This value will be checked by measuring the amplitude of reflected waves off a boundary and then finding the reflection coefficient from these measurements. If the two values obtained for the reflection coefficient are close, then the acoustic impedance measurements will be validated.

Theory

When a sound wave travelling in a liquid hits a boundary with another material, some of the wave is reflected off the boundary. The amplitude of the reflected wave is given by the equation:

R=A_R/A_I

Where R is the reflection coefficient of the boundary, A_R is the amplitude of the reflected wave and A_Iis the amplitude of the incident wave. The reflection coefficient for a particular boundary can be also found using the equation:

R=(Z_1-Z_2)/(Z_1+Z_2 )

Where Z_1 is the acoustic impedance of the material the wave is originally travelling in, and Z_2 is the acoustic impedance of the other material at the boundary. The acoustic impedance is the resistance of a material to sound propagating through it, and can be found using the equation:

Z=vρ

Where v is the speed of sound in the material, and ρ is the density of the material. The speed of the sound can be found experimentally, using the equation v=2d/t where d is the distance from the wave source to the boundary, and t is the time it takes the wave to get from the source to the boundary and back again.

Description of apparatus

The measurements of the amplitude of the reflected waves and the speed of sound in the liquids were made in...

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