Step-by-step explanation:
To find the frequency, we first need to determine the length of the tube.
The length of the tube can be determined using the formula for the wavelength of the nth harmonic in a tube open at one end:
λ = 4L/n
Where:
λ is the wavelength
L is the length of the tube
n is the harmonic number
Given that the 4th harmonic occurs at 63.0 cm, we can rearrange the formula to solve for L:
L = n * λ / 4
Plugging in the values:
n = 4
λ = 63.0 cm
L = 4 * 63.0 cm / 4
L = 63.0 cm
Therefore, the length of the tube is 63.0 cm.
To find the frequency, we can use the formula for the speed of sound in air:
v = f * λ
Where:
v is the speed of sound (which depends on temperature)
f is the frequency
λ is the wavelength
The speed of sound in air at 18°C is approximately 343 meters per second.
To convert the length of the tube to meters:
L = 63.0 cm * (1 m / 100 cm)
L = 0.63 m
Now we can rearrange the formula to solve for frequency:
f = v / λ
f = 343 m/s / 0.63 m
f = 543.65 Hz
Answer : Therefore, the frequency of the 4th harmonic in the given tube at 18°C is approximately 543.65 Hz.