Consider the resonant frequencies of a 1.78 m tube closed at one end at 24°C.
a) Lowest resonant frequency = Hz
HELP: You know the length of the tube. What else do you need in order to calculate the frequency of the lowest resonance of a tube that's closed at one end?
HELP: How does the speed of sound in air depend on the temperature?
b) Frequency differences between successive higher resonances = Hz
HELP: You can calculate the frequencies of successive resonances. They are always the same distance apart, in Hz.
c) Number of higher resonances audible to the humans = (enter an integer)
HELP: 20 kHz is the highest frequency audible to the "normal" ear.
HELP: How many of the differences you calculated in part b) will fit between the lowest resonance and the highest normally audible frequency?
de rosunant in n3-m is 4
a) To calculate the lowest resonant frequency of a tube closed at one end, you need to consider the length of the tube and the speed of sound in air. The formula to calculate the lowest resonant frequency is:
f = v / (2L)
Where f is the frequency, v is the speed of sound, and L is the length of the tube.
To calculate the speed of sound in air at a given temperature, you can use the empirical formula:
v = 331.4 + (0.6 * T)
Where v is the speed of sound in meters per second (m/s) and T is the temperature in degrees Celsius.
In this case, the temperature given is 24°C. So, you can calculate the speed of sound in air by substituting the temperature into the formula:
v = 331.4 + (0.6 * 24)
Once you have the speed of sound, you can then calculate the lowest resonant frequency by substituting the values into the first formula.
b) The frequency differences between successive higher resonances in a tube closed at one end are always the same. This difference is equal to the fundamental frequency (the lowest resonant frequency). So, you can use the value obtained in part a) to calculate the frequency differences between successive higher resonances.
c) To determine the number of higher resonances audible to humans, you need to consider the highest frequency audible to humans and the frequency differences between successive higher resonances. It is mentioned that the highest frequency audible to the "normal" ear is 20 kHz.
From part b), you have the frequency differences between successive higher resonances. Calculate how many of these differences can fit between the lowest resonance (obtained in part a) and the highest audible frequency of 20 kHz.
Divide the difference between the lowest resonance and the highest audible frequency by the frequency difference calculated in part b). Round down to the nearest integer since a resonance cannot be partial. This will give you the number of higher resonances audible to humans.