If the speed of sound in air is 340 m/s, what is approximately the length of a shortest air column closed at one end that will respond to
a tuning fork of frequency 140 Hz? Answer in units of cm.
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To determine the length of the shortest air column that will respond to a tuning fork of frequency 140 Hz, we can use the formula:
Length of air column = (Speed of Sound)/(4 x Frequency)
Given that the speed of sound in air is 340 m/s and the frequency of the tuning fork is 140 Hz, we can substitute these values into the formula:
Length of air column = (340 m/s)/(4 x 140 Hz)
Length of air column = (340 m/s)/(560 Hz)
Now, we need to convert the speed of sound from meters per second (m/s) to centimeters per second (cm/s). Since 1 meter is equal to 100 centimeters, we can multiply the speed of sound by 100 to convert it:
Converted speed of sound = 340 m/s x 100 cm/m
Converted speed of sound = 34000 cm/s
Substituting this into the previous equation:
Length of air column = (34000 cm/s)/(560 Hz)
To get the final answer, we divide the converted speed of sound by the frequency:
Length of air column ≈ 60.71 cm
Therefore, the approximate length of the shortest air column closed at one end that will respond to a tuning fork of frequency 140 Hz is approximately 60.71 cm.
To find the length of a shortest air column closed at one end that will respond to a tuning fork of frequency 140 Hz, we can use the formula:
L = (v / 4f)
Where:
L is the length of the air column
v is the speed of sound in air (340 m/s)
f is the frequency of the tuning fork (140 Hz)
Substituting the given values into the formula:
L = (340 / (4 * 140))
L = 0.6071 m
Converting the length from meters to centimeters:
L = 0.6071 * 100
L ≈ 60.71 cm
Therefore, the approximate length of the shortest air column closed at one end that will respond to a tuning fork of frequency 140 Hz is approximately 60.71 cm.