# Intensity of sound – problems and solutions

1. Point A and B located at 4 meters and 9 meters from a source of the sound. If I_{A} and I_{B} are intensity at point A and point B, then I_{A} : I_{B} =…

__Known :__

The distance of point A from a source of sound (r_{A}) = 4 meters

A distance of point B from the source of sound (r_{B}) = 9 meters

The intensity of sound at point A = I_{A}

The intensity of sound at point B = I_{B}

__Wanted:__ I_{A} : I_{B }

__Solution :__

I_{A} r_{A}^{2} = I_{B} r_{B}^{2}

I_{A} 4^{2} = I_{B} 9^{2}

I_{A }16 = I_{B} 81

I_{A} / I_{B} = 81/16

2. The intensity of a source of sound is 10^{−9 }Wm^{−2}. I_{o} = 10^{−12 }Wm^{−2}. What is the sound level of 10 sources of sounds?

Solution :

__Known :__

I = 10^{-9} W/m^{2}

I_{o} = 10^{-12} W/m^{2}

x = 10

__Known:__ Sound level (β)

__Solution :__

3. The sound level of a source of sound is 10 dB. What is the intensity of 1000 sources of sound? The minimum intensity I_{o} = 10^{−12} Wm^{−2}.

__Known :__

β = 10 dB

I_{o} = 10^{-12} W/m^{2}

x = 1000

__Wanted__ : Intensity

__Solution :__

The intensity of a source of sound :

The intensity of 1000 sources of sound :

I = (1000)(10^{-11}) = (10^{3})(10^{-11})

I = 10^{-8 }W/m^{2}

4. The sound level of A is 40 dB, and the sound level of B is 60 dB. I_{o} = 10^{-12} W m^{-2}. Determine 100β_{A} : 10β_{B}.

__Known :__

The sound level of A = 40 dB

The sound level of B = 60 dB

I_{o} = 10^{-12} W m^{-2}.

__Wanted ____:__ 100β_{A} : 10β_{B}

__Solution :__

The sound level of 100 A :

β = 40 + 10 log 100

β = 40 + 10 log 10^{2}

β = 40 + (2)(10)(log 10)

β = 40 + (2)(10)(1)

β = 40 + 20

β = 60 dB

The sound level of 10 B :

β = 60 + 10 log 10

β = 60 + 10 log 10^{1}

β = 60 + (1)(10)(log 10)

β = 60 + (1)(10)(1)

β = 60 + 10

β = 70 dB

β_{A} : β_{B}

60 : 70

6 : 7

5. If point P is the source of sound, then the ratio of sound intensity at points S, R, and Q is …

__Known :__

The distance of point Q from the sound source (r_{Q}) = 3 meters

The distance of point R from the sound source (r_{R}) = 6 meters

The distance of point S from the sound source (r_{S}) = 5 meters

Sound intensity at point Q = I_{Q}

Sound intensity at point R = I_{R}

Sound intensity at point S = I_{S}

Wanted:__ Comparison of sound intensity at points S, R, and Q (I___{S}: I_{R}: I_{Q})

__Solution :__

Sound intensity at point S :

Sound intensity at point R :

Sound intensity at point Q :

Comparison of sound intensity at points S, R, and Q :

6. Point A is P from the sound source, point B is 2P from source sound and point C is 4P from the sound source. Comparison of sound intensity at A, B, and C is …

__Known :__

Distance point A from the sound source (r_{A}) = P

Distance point B from sound source (r_{B}) = 2P

Distance point C from sound source (r_{C}) = 4P

Sound intensity at point A = I_{A}

Sound intensity at point B = I_{B}

Sound intensity at point C = I_{C}

__Wanted:__ Comparison of sound intensity at A, B, and C (I_{A} : I_{B} : I_{C})

__Solution :__

Sound intensity at point A :

Sound intensity at point B :

Sound intensity at point C :

Comparison of sound intensity at A, B, and C :

7. A total of 100 people were singing. If the level of the sound intensity of one student when singing 40 dB (assuming for each child is the same), then the intensity of the resulting sound is … (I_{o} = 10^{-12} W.m^{-2})

__Known :__

Level of the intensity of one student (TI) = 40 dB

I_{o} = 10^{-12} W/m^{2}

The number of students (x) = 100

Wanted:__ The sound intensity of 100 students__

__Solution :__

Sound intensity of a student :

Sound intensity of 100 students :

I_{x} = (x)(I)

I_{x} = (100)(10^{-8}) = (10^{2})(10^{-8})

I_{x} = 10^{-6 }W/m^{2}

8. The sound intensity of 100 identical machines is 10^{-7} Watt.m^{-2}. If I_{o} = 10^{-12 }Watt.m^{-2}, then the level of the sound intensity of a machine is…

__Known :__

Sound intensity of 100 machines (I_{x}) = 10^{-7} Watt.m^{-2}

I_{o} = 10^{-12} W/m^{2}

The number of machines (x) = 100 = 10^{2}

W__anted :__ The sound intensity level of a machine (TI)

__Solution :__

Sound intensity of a machine :

I_{x} = (x)(I)

10^{-7} = (10^{2})(I)

I = 10^{-7 }/ 10^{2} = (10^{-7})(10^{-2}) = 10^{-9 }

The level of sound intensity of a machine (TI) :

9. The sound intensity of a source of sound is 6 x 10^{-6} W/cm^{2}. If the sound intensity level increased by 10 db, determine the intensity of sound.

__Known :__

Intensity (I) = 6 x 10^{-6 }W/cm^{2 }

I_{o} = 10^{-12} W/m^{2 }= 10^{-12} W / 10^{4} cm^{2 }= 10^{-16} W/cm^{2}

__Wanted :__ The intensity of sound

__Solution :__

The addition of the sound intensity of 10 W/m^{2} = 10^{-3} W/cm^{2} is equivalent to the addition of the sound intensity level of 10 dB. The addition of sound intensity of 10^{2} W/m^{2 }= 10^{-2 }W/cm^{2} is equivalent to the addition of sound intensity level of 20 dB. And so on.

If the intensity level is increased by 10 dB, the intensity increases by 10^{-3} W/cm^{2}. So the intensity becomes 6 x 10^{-6} W/cm^{2}) + (10^{-4} W/cm^{2}) = (6 x 10^{-6} W/cm^{2}) + (100 x 10^{-6} W/cm^{2}) = 106 x 10^{-6} W/cm^{2}.

10. Observer A is 5 m away from a sound source. While observer B is 10 m from the same sound source. So the ratio of sound intensity heard by observer B and A is…

__Known :__

The distance of A from the source of sound (r_{A}) = 5 meters

The distance of B from the source of sound (r_{B}) = 10 meters

__Wanted:__ The ratio of sound intensity heard by observer B and A

__Solution :__

I_{B} : I_{A} = 1 : 4

The correct answer is B.