Male Rana catesbeiana bullfrogs are known for their loud mating call. The call is emitted not by

Male Rana catesbeiana bullfrogs are known for their loud...

Key Concepts

Decibel Scale

The decibel scale is a logarithmic measure of sound pressure or intensity relative to a reference level. It allows comparisons between very different sound energy levels in a compact numerical range, where a small change in decibels can represent a large change in actual intensity.

Sound Intensity

Sound intensity quantifies the energy carried by a sound wave per unit area per unit time. It is a critical concept in acoustics because it relates the measurable sound pressure to the energy that is being transmitted through a medium.

Pressure Amplitude

Pressure amplitude is the measure of the maximum variation in pressure caused by a sound wave relative to the ambient pressure. It is directly related to the intensity of the sound and plays a key role in determining how much the medium (or a structure like an eardrum) is displaced by the sound.

Frequency and Angular Frequency

Frequency is the number of oscillations or cycles per second of a wave. Angular frequency, which is derived from the frequency by multiplying by 2?, is used in many wave equations to relate the temporal rate of oscillation to spatial displacement and other dynamic parameters.

Acoustic Impedance and Displacement Relationship

Acoustic impedance is a property of the medium that links pressure variations to the corresponding particle velocity. Through the relationship p = ?c??, where p is the pressure amplitude, ? is the density of the medium, c is the speed of sound, ? is the angular frequency, and ? is the displacement amplitude, one can determine how far particles in the medium oscillate in response to a given sound pressure.

Transcript

00:01 So frog's ear creates a sound with a frequency of 270 hertz and the sound level of and once we replace this we get row v2 pi squared row v f squared rau v f squared let me rewrite this here.

00:38 So it is 2 pi squared row with f squared s m.

00:47 And from here we can this wave is 85 decibel, decibel and we need to find what is what is the amplitude of the membrane, which causes the sound wave amplitude of oscillation so for an intensity we have a formula we can find oh and then it's done marat oh so frogs ear creates a sound with a frequency of two hundred seven seventy hertz and the sound level of where intent marato so frog's ear creates a sound with a frequency with a frequency of the frequency of the where sm is the maximum displacement of a molecule in the air but while we're considering the nearby molecules to this membrane this wave is 85 decibel and we need to find what is what is the amplitude of the membrane which causes the sound wave amplitude of oscillation so for an intensity we have a formula is 85 decibel decibel and we need to find find what is what is the amplitude of the membrane membrane which causes the sound wave amplitude of oscillation so for an intensity we have a form formula where intense these molecules displacements would be the same as the displacement of this membrane so we need to find this quantity in the the end but first we don't know what is omega but we know the frequency and relation between them is straightforward so we just replace omega by by where intensity of a sound wave is one half row v omega squared s m squared where sm is the maximum displacement of a molecule in the air but while we're considering the nearby molecules to this membrane this frequency city of a sound wave is one half row v omecus squared s m squared where sm is the maximum displacement of a molecule in the air but while we're considering the nearby molecules to this membrane this and it is 2 pi f and we get intensity 2 pi squared raw v f squared sm squared and from here our amplitude squared is intensity and this molecules displacements would be the same as the displacement of this membrane so we need to find this quantity in the end but first, we don't know what is omega, but we know the frequency and relation between them is straightforward, so we just replace omega by 2 pi square.

06:46 This molecule's displacements would be the same as the displacement of this membrane.

06:55 So we need to find this quantity in the end.

07:03 But first, we don't know what is omega, but we know the frequency and relation between them is straightforward.

07:13 So we just replace omega by frequency.

07:18 And row v.

07:22 F squared.

07:23 And we are halfway done we just need to find out what is the intensity here and plug this number here so we need to use the second number level of sound level in the frequency and it is 2xf and it is 2xf and we get intensity 2 pi squared raw vf squared s m squared and from here our amplitude squared is intensity and to let's ev else to find out and it is 2 pi f and we get intensity 2 pi squared raw v f squared s m squared and from here our amplitude squared is intensity and 2 pi squared what is the intensity so the sound level is defined by this formula which is logarite intensity over some threshold intensity which is the minimum intensity human human error could detect and e pi squared row v f squared and we are halfway done we just need to find out what is the intensity here and plug this now number here so we need to use the second number level of sound level in that it is row v f squared and we are halfway done we just need to find out what is the intensity here and plug this number here here here so we need to use the second number level of sound level in decibels to find out 10 to the minus 12 watts meter square yes and we know that this beta is 85 decibel and we can write at logarith to find out what is the intensity so the sound level is defined by this formula which is logarite intensity over some threshold intensity which is the minimum intensity human human air could detect and it what is the intensity so the sound level is defined by this formula, which is logarite intensity over some threshold intensity, which is the minimum intensity human air could detect.

12:11 And it is 8 .5.

12:27 This means that this fraction becomes 10 to the 8 .5 power, which is square root of tis 10 to the minus 12 watts, yes.

12:58 And we know that this beta is 85 decibel and we can write that loggerid 10, 10 to the minus 12 watts meter squared, yes.

13:31 And we know that this beta is 85 decibel and we can write that logarite 10 to the 8 and square root of 10 is 3 .16 8 watt meters now is 8 .5 this means that this fraction becomes 10 to the 8 .5 power, which is square of...

14:57 Is 8 .5.

15:11 This means that this fraction becomes 10 to the 8 .5 power, which is a square.

15:27 Square root of 10 and once we know this threshold intensity is this we can easily find what is the intensity and it is 3 .16 10 to the minus 4 what's meter squared so this is a fraction so there there shouldn't be any units here 10 to the 8 and square root of 10 is 3 .16, 10 to the 8 watts to the 8 watts meter squared.

16:32 Now let me 10 to the 8 and square root of 10 is 3 .16, 10 to the 8, what what's.....

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