Ratio of amplitudes of sound problem

In summary, the ratio of amplitudes of sound is a comparison of the loudness of two sounds, measured using a decibel scale. Factors such as distance, frequency, and environment can affect this ratio. It is important for understanding sound intensity and has applications in industries such as music and construction. It is also used in fields like acoustics, engineering, medicine, and animal communication.
  • #1
Amith2006
427
2
Sir,
The intensity level due to 2 waves of same frequency in a given medium is 1 bel and 4 bel. What is the ratio of their amplitudes?
I solved it in the following way:
L1 = 10 decibels
L2 = 40 decibels
Loudness(L) = 10(log(I/Io))
Where I= Intensity of sound, Io = Intensity of weakest audible sound
Therefore,
10 = 10[log(I1/Io)]
Similarly,
40 = 10[log(I2/Io)]
Solving we get,
I1 = 10 Watt/m^2
I2 = 10000 watt/m^2
Intensity is proportional to (amplitude)^2
I1/I2 = a1^2/a2^2
a1/a2 = [I1/I2]^(1/2)
i.e. a1/a2 = [1/1000]^(1/2)
= 1/[10^(3/2)]
Is it right?
 
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  • #2
Sounds good to me.
 

Related to Ratio of amplitudes of sound problem

What is the ratio of amplitudes of sound?

The ratio of amplitudes of sound is a comparison between the loudness of two sounds. It is calculated by dividing the amplitude, or maximum displacement of a sound wave, of one sound by the amplitude of another sound.

How is the ratio of amplitudes of sound measured?

The ratio of amplitudes of sound is measured using a decibel scale. This scale is logarithmic, meaning that a small change in decibels represents a large difference in sound intensity. The ratio of amplitudes of sound is calculated by converting the sound pressure level to decibels and then taking the difference between the two sound levels.

What factors can affect the ratio of amplitudes of sound?

The ratio of amplitudes of sound can be affected by a variety of factors such as distance from the sound source, frequency of the sound, and the environment in which the sound is being measured. Other factors such as obstacles and reflections can also impact the ratio of amplitudes of sound.

Why is the ratio of amplitudes of sound important?

The ratio of amplitudes of sound is important because it helps us understand the loudness and intensity of sound. It allows us to compare and measure the differences between sound levels, which can be crucial for industries such as music and construction where sound levels need to be carefully controlled.

What are some real-world applications of the ratio of amplitudes of sound?

The ratio of amplitudes of sound is used in various fields such as acoustics, engineering, and medicine. It is used to measure and control noise levels in buildings, determine the loudness of musical instruments, and diagnose hearing impairments. It is also used in the development of noise-cancelling technology and in the study of animal communication.

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