Sound Intensity of a howler monkey

In summary, the howler monkey is the loudest land animal, with a sound that can be heard up to a distance of 1.4 km. The intensity level of a howler's call at 49 dB can be calculated using the inverse square law and the definition of decibels, resulting in a distance of approximately 5 m. This can be used to determine the answer to a similar problem on an old exam, where a howler's call at 28 dB can be heard at a distance of 140 m.
  • #1
Soaring Crane
469
0

Homework Statement


The howler monkey is the loudest land animal and can be heard up to a distance of 1.4 km. Assume the acoustic output of a howler to be uniform in all directions. The distance at which the intensity level of a howler's call is 49 dB, in SI units, is closest to:

a. 6.0---b.9.9----c. 8.4----d.7.5---e. 5.0


Homework Equations


The only formula that I think is adequate in the inverse squares law in which:

I/I_o = r_2^2/r_1^2, where r is the distance and I is intensity in W/m^2



The Attempt at a Solution



I only know of two values being given:
I = 49 dB = 0.4083 W/m^2
r_1 = 1.4 km

Is the third value I_o suggested anywhere in the problem? How do I use the above formula?

Thanks.
 
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  • #2
Soaring Crane said:

Homework Equations


The only formula that I think is adequate in the inverse squares law in which:

I/I_o = r_2^2/r_1^2, where r is the distance and I is intensity in W/m^2
Yes, you'll need the inverse square law. But you'll also need to know how to go from decibels to intensity ratios. Look up the definition of decibel.

Also: Does the problem state 29 or 49 db? (I suspect that the 29 db was a typo.)
 
  • #3
Sorry, it's 49 dB.

I converted the dB into W/m^2, but I don't know what is meant by corresponding it to the intensity ratio.
 
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  • #5
Let me retype the law again:

I_1/I_2 = r_2^2/r_1^2

The reason why I was confused before is that must I use I_o for I_1?

I_o is standarad, so, since another I value is not given, must I use I_o?
 
  • #6
I_0 would be the intensity at 1.4 km--where the sound can barely be heard.
 
  • #7
This is what I did so far:

I_1= 10^-12 W/m^2
I_2 = .4083 W/m^2
r_1 = 1.4 km
r_2 = ?

sqrt{(10^-12)/(.4083)W/m^2]*(1400 m)^2} = r_2

r_2 = .00219 km??/

What did I do wrong?
 
  • #8
Soaring Crane said:
This is what I did so far:

I_1= 10^-12 W/m^2
I_2 = .4083 W/m^2
Where did you get that value for I_2?

All you really need is the ratio of the intensities. That's where the dB value comes in.
 
  • #9
I divided 49 dB by 120 dB according to the units for W/m^3.
 
  • #10
Soaring Crane said:
I divided 49 dB by 120 dB according to the units for W/m^3.
Sorry, but I don't understand this.

Did you look at the link I gave you in post #4? The equation that you need (in addition to the inverse square law that you already know) is the definition of the decibel scale of intensity:
I(in dB) = 10 log(I/I_0)
 
  • #11
i need to no whether its 49 dbspl or dbsil or swl...
 
  • #12
this is just an attempt takin 0dbspl i.e., the threshold of hearing at the 1.4th km or 1400m... wil get 4.96m .. i.e., approx option (e)5...this can be done using the inverse square law...
L2=L1-20logD2/D1 where L2=49dbspl, L1=0dbspl, D2=1400 and D1 is got as 4.96.. i hope this is rite
 
  • #13
Looks good to me.
 
  • #14
Hey, I am taking Physics II and this is a problem on an old exam. Follow this setup with your own numbers and you should be golden

Question:
The howler monkey is the loudest animal and can just be heard at a distance of 3.6km (threshold of hearing s 10^-12 /m^2). Assume the acoustic output of a howler monkey to be uniform in all directions. How far are you from the monkey if the intensity level is 28 dB at your location?

a: 210m
b: 140m
c: 290m
d: 170m
e: 240m

Solution:

1st Step: Definition of Intensity Levels
/beta=10dBlog(I/I_o) ---> rearrange: I=I_o(10^(/beta/10))---> I=(1x10^-12)(10^2.8)= 6.31x10^-10 W/m^2

2nd Step: Inverse Law

(I/I_0)=(r_1^2/r_2^2)--->rearrange: r_2=Square((r_1^2)(I_o)/(I))
I=6.31x10^-10 W/m^2
I_o= 1x10^-12 W/m^2
r_1= 3.6km~~3600m

r_2=Square((3600m^2)(1x10^-12 W/m^2)/(6.31x10^-10 W/m^2))
r_2=146.5m

Answer is closest to (B)
 

Related to Sound Intensity of a howler monkey

What is the sound intensity of a howler monkey?

The sound intensity of a howler monkey can vary depending on the individual and the situation. However, on average, the sound intensity of a howler monkey can range from 90-110 decibels, which is similar to the sound intensity of a lawnmower.

How does the sound intensity of a howler monkey compare to other animals?

The sound intensity of a howler monkey is one of the loudest among land animals. It is surpassed only by the blue whale, hippopotamus, and lion. In fact, the howler monkey's loud howls can be heard up to 3 miles away in the rainforest.

What factors can affect the sound intensity of a howler monkey?

The sound intensity of a howler monkey can be affected by a variety of factors, such as the size and health of the individual, the distance from the source of the sound, and the surrounding environment. Additionally, the intensity of the howls can also vary depending on the purpose of the vocalization, whether it is for communication or to establish dominance.

Is the sound intensity of a howler monkey harmful to humans?

The sound intensity of a howler monkey can be loud and startling, but it is not harmful to humans. However, prolonged exposure to loud noises, including the howls of a howler monkey, can potentially damage hearing. It is important to use ear protection if you are frequently exposed to loud sounds.

How is the sound intensity of a howler monkey measured?

The sound intensity of a howler monkey can be measured using a sound level meter, which measures the decibels of a sound. However, due to the complex nature of the howler monkey's vocalizations, it can be difficult to accurately measure their sound intensity in the wild. Scientists often use specialized equipment and techniques to capture and analyze the sound intensity of howler monkeys in their natural habitat.

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