what is the length of the shortest pipe closed on one end that will have a fundamental frequency of 60 hz on a day when the velocity of sound is 340 m/s?
To find the length of the shortest pipe closed on one end with a fundamental frequency of 60 Hz, we can use the equation:
v = λf
Where:
v is the velocity of sound (340 m/s)
λ is the wavelength of the sound wave
f is the frequency (60 Hz)
First, we need to find the wavelength (λ). The fundamental frequency of a closed pipe is given by the equation:
λ = 4L
Where:
L is the length of the pipe
Rearranging the equation, we have:
L = λ/4
Substituting the given fundamental frequency into the equation, we get:
L = (340 m/s) / (4 * 60 Hz)
L = 0.1417 meters
Therefore, the length of the shortest pipe closed on one end that will have a fundamental frequency of 60 Hz is approximately 0.1417 meters.
To determine the length of the shortest pipe closed on one end that will have a fundamental frequency of 60 Hz, we can use the formula for the wavelength of a sound wave in a pipe:
λ = 4L/3
Where λ is the wavelength and L is the length of the pipe. For a closed-end pipe, the fundamental frequency corresponds to a quarter wavelength, so we can rewrite the formula as:
λ = 4L
To find the length L, we need to first calculate the wavelength of the sound wave at 60 Hz. The formula for the wavelength of a wave is:
λ = v/f
Where λ is the wavelength, v is the velocity of sound, and f is the frequency.
Let's plug in the values:
v = 340 m/s (given)
f = 60 Hz (given)
λ = 340 m/s / 60 Hz = 5.67 m
Now, we have the wavelength (λ) and we know that for a closed-end pipe, the fundamental frequency corresponds to a quarter wavelength. So, we can calculate the length (L) as follows:
L = λ / 4 = 5.67 m / 4 = 1.42 m
Therefore, the length of the shortest pipe closed on one end that will have a fundamental frequency of 60 Hz, when the velocity of sound is 340 m/s, is approximately 1.42 meters.