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Chapter 17: Q33P (page 508)

Male Rana catesbeiana bullfrogs are known for their loud mating call. The call is emitted not by the frog鈥檚 mouth but by its eardrums, which lie on the surface of the head. And, surprisingly, the sound has nothing to do with the frog鈥檚 inflated throat. If the emitted sound has a frequency of 260Hzand a sound level of85dB(near the eardrum), what is the amplitude of the eardrum鈥檚 oscillation? The air density is1.21kg/m3.

Short Answer

Expert verified

The eardrum鈥檚 oscillations has the amplitude of 0.76鈥夆赌坝纠.

Step by step solution

01

Given

  1. Frequency: f = 260 Hz
  2. Air density:蚁=1.21鈥塳驳/尘2
  3. Level of intensity:尾=85鈥塪叠
02

Determining the concept

Find the sound intensity using the formula for the sound level in terms of intensity. Write the amplitude in terms of intensity, density, frequency and speed of sound.

Formulae are as follow:

尾=10logII0

I=12蚁v(2蟺蹿)2A2

where, I,I0 are intensities, f is frequency, A is area,蚁 is density and v is density.

03

Determining the amplitude of the eardrum’s oscillation 

From the formula for sound level,

尾=10logII0

I=I0100.1尾=(10鈭�12鈥塛/尘2)(108.5鈥塪叠)=3.162脳10鈭�4W/m2

Since, intensity of sound is defined as,

I=12蚁v(2蟺蹿)2A2

A=2I蚁v(2蟺蹿)2=2脳(3.162脳10鈭�4鈥塛/m2)(1.21鈥夆赌塳驳/m3)(340鈥尘/s)(2脳3.14脳260鈥塇锄)2=0.76鈥夆赌坝纠

Hence, the oscillations has the amplitude equal to0.76鈥夆赌坝纠 .

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