# Introduction to Acoustics

On this page you will find the answers to the exercises in the booklet 'Introduction to Acoustics', Fifth Edition by Mark Huckvale.

## Chapter One

1. Fill in the blanks:

1. The frequency of a periodic event is measured in hertz.
2. An event that repeats 1000 times per second has a frequency of 1kHz.
3. The density of air is about 1kgm−3.
4. An event that repeats 10,000 times per second has a period of 100µs.
5. 5cm is 5x10−2m = 0.05m.

2. Express the following in scientific notation to three significant figures:

1. 61743 = 6.17 x 104
2. 20000 = 2.00 x 104
3. 0.02 = 2.00 x 10−2
4. 1/500 = 2.00 x 10−3
5. 1/0.05 = 2.00 x 101
6. 2556 x 10−4 = 2.56 x 10−1
7. 0.0564 x 10 = 5.64 x 103

3. Simplify the following:

1. 104 x 105 = 109
2. 104 x 10-3 = 101
3. 10−6 x 103 x 10 = 10−2
4. 101 ÷ 10−3 = 104

## Chapter Two

1. Given the following (approximate) logarithms to base 10:

log(2) = 0.3; log(3) = 0.48; log(4) = 0.6; log(5) 0.7

Find approximate solutions to the following sums without using a calculator:

1. log(100) = 2
2. log(0.01) = −2
3. 100 = 1
4. 100.3 = 2
5. log(6) = 0.3 + 0.48 = 0.78
6. log(0.25) = −log(4) = −0.6
7. log(2/3) = 0.3 − 0.48 = −0.18
8. 101.7 = 101 x 100.7 = 50

2. The following measurements were made from a straight line graph:

When X is 0, Y = 12

Change in Y for 4 units along the X axis = 3.2

1. What is the equation of the line?

Y = 0.8X + 12

2. What is the value of Y when X is 20?

28

3. What is the value of X when Y is 20?

10

## Chapter Three

1. How much chocolate would I need to spread over a 1m2 surface to generate a pressure underneath of 1Pa? (assume g=10ms−2) If I spread that amount of chocolate over 1/20 of the area, how does the pressure change?

• Pressure = Force / Area
• Force = Mass x Acceleration
• Therefore: Mass = Pressure x Area / Acceleration
• Mass = 1 x 1 / 10 = 0.1kg
• Reducing the area by 20 increases the pressure by 20 for a fixed size force.

2. Winding a grandfather clock involves lifting a weight of 250g up a distance of 0.8m. Taking the acceleration due to gravity (g) to be 10ms−2, how much more energy does the fully wound clock have over the fully unwound one?

• Energy = Force x Distance
• Force = Mass x Acceleration
• Therefore: Energy = Mass x Acceleration x Distance
• Energy = 0.25 x 0.8 x 10 = 2J

3. If the intensity of a sound at 2m from the source is 10Wm−2 , what would be the intensity at 6m from the source if the energy was radiated equally in all directions? (Hint: the total power at 2m is distributed over the surface of a sphere of radius 2m, but the total power at 6m is distributed over the surface of a sphere of radius 6m).

• Intensity = Power / Area
• Power = Intensity x Area
• Call the area of the sphere at 2m = A
• Then Power = 10W x A
• When sphere grows to 6m, radius increases by x3
• But Area increases by x9 = 9 x A
• Therefore Intensity at 6m = (10W x A) / (9 x A) = 1.1W
• Intensity falls as the square of the distance to the source: this is called the inverse square law.

 © 2003 Mark Huckvale University College London