Sound enters the ear, travels through the auditory canal, and reaches the eardrum. The auditory canal is approximately a tube open at only one end. The other end is closed by the eardrum. A typical length for the auditory canal in an adult is about 2.6 cm. If the speed of sound is 338 m/s. What is the fundamental frequency of the canal? (Interestingly, the fundamental frequency is in the frequency range where human hearing is most sensitive.)
f1=c/(4L)
c=338m/s
L=2.6cm=0.026m
f1=338/(4x0.026)
=3250Hz
Oh, the fundamental frequency of the auditory canal, you say? Well, let me put on my musical hat for a moment. You see, the fundamental frequency refers to the lowest frequency at which a vibrating object, in this case, the auditory canal, naturally resonates.
Now, if we consider the length of the auditory canal, which is approximately 2.6 cm, we can use this information to calculate the fundamental frequency. But first, let me dust off my math skills and get cracking!
To calculate the fundamental frequency, we need to remember that frequency is inversely proportional to the wavelength of the sound wave. The wavelength, in turn, is related to the length of the auditory canal. So, we can use the formula:
Fundamental frequency = Speed of sound / Length of the auditory canal
Given that the speed of sound is 338 m/s and the length of the auditory canal is 2.6 cm (or 0.026 m, if you prefer), we can plug these values into the formula:
Fundamental frequency = 338 m/s / 0.026 m
And after some delightful number crunching, we discover that the fundamental frequency of the auditory canal is approximately 13,000 Hz!
So, there you have it! The fundamental frequency of the auditory canal is approximately 13,000 Hz, and that's right in the sweet spot of human hearing sensitivity. Now, if you'll excuse me, I think I hear a circus jingle that needs my attention. Ta-ta!
To find the fundamental frequency of the auditory canal, we can use the formula:
Fundamental frequency = Speed of sound / Length of the canal
Given:
Speed of sound = 338 m/s
Length of the canal = 2.6 cm = 0.026 m
Plugging the values into the formula:
Fundamental frequency = 338 m/s / 0.026 m
Fundamental frequency ≈ 13000 Hz
Therefore, the fundamental frequency of the auditory canal is approximately 13000 Hz.
To find the fundamental frequency of the auditory canal, we can use the formula:
Fundamental frequency = Speed of sound / Length of the auditory canal
Given that the speed of sound is 338 m/s and the length of the auditory canal is 2.6 cm (which needs to be converted to meters), we can proceed with the calculation.
Converting the length of the auditory canal to meters:
2.6 cm = 2.6 / 100 meters (since 1 meter = 100 cm) = 0.026 meters
Now we can substitute the values into the formula:
Fundamental frequency = 338 m/s / 0.026 meters
Calculating this:
Fundamental frequency = 13,000 Hz
Therefore, the fundamental frequency of the auditory canal is 13,000 Hz.
Assume it is 1/4 lambda, closed at one end.
1/4 lambda= .025m
lambda= .1m
f= 338/.1= 3380hz.