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Sound Intensity is defined as the power of sound per unit area. Sound Intensity is represented by I. The SI unit of sound intensity is W/m2. The intensity of sound depends on the surface of the source of the sound. It describes the rate of energy flow through a unit area. Sound intensity is a vector quantity with both magnitude and direction. Sound Intensity is affected by two factors namely the amplitude of the sound waves and how far the sound waves have traveled from the source of the sound.
Sound Intensity Formula is given as I = P/A, where, P denotes sound/acoustic power and A refers to the normal area to the direction of propagation. The physiological intensity or sound sensation is measured in decibels (dB).
Read More: NCERT Solutions for Class 11 Physics Waves
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Key Terms: Sound Intensity, Sound, Power, Acoustic Power, Decibels, Sound Sensation, Sonority, Kinetic Energy
What is Sound Intensity?
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Sound Intensity is referred to the sound per unit area perpendicular to the path of the sound waves. According to the standard definition, it refers to the calculation of noise sound intensity in the air at the listener's position as a quantity of sound energy. Sound Intensity is represented by the symbol “I” and has the SI Unit W/m2 (watt per square meter).
- The increasing amplitude of the source of the sound and that of the vibrating surface causes the kinetic energy of the mass of air.
- The kinetic energy then increases with the mass of air into vibration and with its average speed.
- The intensity of perception of a sound by the ear also depends upon the distance from the source of the sound.
- Sound Intensity is also affected by the nature of the elastic medium between the source of a sound and the ear.
- Sonority is the intensity of the sound that is perceived subjectively which allows sounds to be arranged from the loudest to the weakest.
Sound Intensity
Sound Intensity Formula
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The Sound Intensity Formula is given as:
| \(I = \frac{P}{A}\) |
Where
- I refers to the Sound Intensity.
- P refers to the Sound/Acoustic Power.
- A refers to the Normal area to the direction of propagation.
Read More: Sound Important Questions
To measure the sound intensity level, we need to compare the given sound intensity value with the standard intensity value. The formula for Sound Intensity Level is given as follows:
| \(I_L = 10log_{10} \frac{I}{I_0}\) |
Where
- I refers to Sound Intensity.
- Io refers to the Reference Intensity.
- The unit of sound intensity is expressed in decibels (dB).
The intensity of sound is measured in the units of decibels (dB). The scale of sound sensation is logarithmic, which means that an increase of 10 dB will correspond to an intensity of 10 times greater.
Solved ExampleExample: A boy whistles with a power of 0.9 ×10−4 W. What will be the sound intensity at a distance of 7 meters? Solution: According to the question,
Using the Sound Intensity Formula, I = P/A I = (0.9×10−4) / 7 I = 1.28 ×10−5 W/m2 Thus, the sound intensity will be 1.28 ×10−5 W/m2. |
Things to Remember
- Sound Intensity is the power carried by sound waves per unit area in a direction perpendicular to that area.
- It is also referred to as Acoustic Intensity.
- Sound Intensity is the power of the sound in Watts divided by the area the sound covers in square meters.
- The SI Unit of Sound is and is represented by I.
- Sound Intensity Formula is I = P/A. Here P refers to acoustic power and A refers to the area.
Previous Years’ Questions
- 90 dB sound is x times more intense than 40 dB sound, then x is…
- The SI unit of intensity of the wave is… (UP CPMT 2012)
- A sound source S is moving along a straight track with speed… (JEE Main 2020)
- A siren emitting a sound of frequency 800 Hz moves away from… (NEET 2016)
- A source of sound is moving with a velocity of… (KCET 2016)
- Dopplers effect in sound takes place when source and observer… (VMMC Medical 2007)
- The velocity of sound waves in a medium does not depend on… (UPSEE 2019)
- The velocity of sound waves in air is 330m/s. For a part… (AIIMS 2013)
- Sound waves transfer… (KCET 2009)
- Sound waves travel fastest in…
Sample Questions
Ques. A person is cheering at a concert at a power of 2×10-4 W. What will be the sound intensity at a distance of 10 m? (3 Marks)
Ans. Given parameters are:
- Power (P) = 2 ×10-4
- Area (A) = 10 m
Using Sound Intensity Formula,
I = P / A
I = 2×10-4 / 10
I = 2×10-5
Thus, the sound intensity will be 2×10-5 W/m2.
Ques. A boy calls out to his mother from his room which is 20m away from his mother’s room. He calls her at a sound intensity of 1.1×10-4. What will be the power that he called from if his mom heard the same? (3 Marks)
Ans. According to the question,
- Sound Intensity (I): 1.1×10-4
- Area (A) : 20 m
Rearranging the Sound Intensity Formula, we get
P = I × A
P = 1.1 ×10-4×20
P = 2.2×10-3
Thus, the boy called his mom at a power of 2.2×10-3 W.
Ques. Calculate the intensity level which is equivalent to an intensity of 1 nW/m2. (3 Marks)
Ans. The Intensity Level formula is given as follows:
IL = 10log10I/I0
Given that,
- I = 1 nWm2 = 1 × 10-9 Wm2
- Io = 10-12 Wm2
Substituting the values,
IL= 10 log10 (1×10-9) / 10-12
IL = 10 log10 103
IL = 30
Thus, the intensity level is 30 dB.
Ques. Calculate the intensity of the siren of a police jeep with a power of 8×10-4 at a distance of 30m. (3 Marks)
Ans. Given parameters are:
- Power (P) = 8 ×10-4
- Area (A) = 30m
Using the Sound Intensity Formula,
I = P / A
I = 8×10-4 ×30
I = 0.024
Hence, the sound intensity in the given condition will be 0.024 W/m2.
Ques. Calculate the level of sound sensation in decibels corresponding to an intensity wave 10-10 W/m2. (3 Marks)
Ans. The intensity of sound is already given in the question, thus, we can easily calculate the sound sensation.
I = 10-10 W/m2
Sound Sensation (S) = 10*log(I/I0) = 10*log(10-10W/m2/0-12 W/m2)
S = 20 dB
Thus, the level of sound sensation in decibels is 20 dB.
Ques. Calculate the distance between two people if one calls the other at a sound power of 5×10-4 at 10×10-4 sound intensity. (3 Marks)
Ans. According to the question,
- Sound Power (P) = 5×10-4
- Sound Intensity (I) = 10×10-4
On rearranging the Sound Intensity Formula,
A = P / I
Now, substitute the values of P and I,
A = 5×10-4 / 10×10-4
A = 0.5 m
Therefore, the distance between both persons is 0.5m.
Ques. Calculate the sound intensity of a vocalist who is singing at a power of 6×10-4 relative to a person at a distance of 3m. (3 Marks)
Ans. Given parameters are:
- Power (P) = 6×10-4
- Area (A) = 3×10-4
According to the Sound Intensity Formula,
I = P / A
I = 6×10-4 / 3
I = 2×10-4
Hence, the sound intensity in this particular case will be 2×10-4 W/m2.
Ques. Determine the power generated if the normal propagation area is 20 km2 and the sound intensity is 10-10 W/m2. (3 Marks)
Ans. Given that,
- I = 10-10 W/m2
- A = 20km2 = 20x106m2
Using Sound Intensity Formula,
I = P/A
Rearranging it,
P = I x A
P = 10-10 W/m2 x 20*106 m2
P = 2 x 10-3 W
Ques. What is meant by the intensity of sound waves? (3 Marks)
Ans. The intensity of the sound wave refers to the amount of energy that is transported past a given area of the medium per unit of time. The greater the amplitude of vibrations of the particles of the medium would be, the greater would be the rate at which energy is transported through it, and the more intense would the sound wave.
Ques. What is meant by the intensity of sound in Physics? (3 Marks)
Ans. The intensity of a sound refers to the power of the sound in Watts divided by the area the sound covers in square meters. The loudness of a sound is related to the intensity of any given sound to the intensity at the threshold of hearing. The intensity of sound is measured in decibels (dB).
Ques. Mention the three types of sound. (3 Marks)
Ans. The three types of sound are as follows:
- Infrasonic: Sound with a frequency of less than 20Hz is referred to as infrasonic sound.
- Sonic: Sound with a frequency between 20 to 20,000Hz is referred to as sonic sound.
- Ultrasonic: Sound with a frequency of more than 20,000Hz is referred to as ultrasonic sound.
Ques. What factors affect sound intensity? (2 Marks)
Ans. The intensity of sound is affected by two factors:
- Amplitude of the sound waves
- How far the sound waves have traveled from the source of the sound
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