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 134 Hz?
Answer in units of cm.
To find the length of the shortest air column that will respond to a tuning fork of a specific frequency, we can use the formula:
\[ L = \frac{v}{2f} \]
where:
L = length of the air column (in meters)
v = speed of sound in air (in meters per second)
f = frequency of the tuning fork (in Hertz)
Given:
v = 340 m/s
f = 134 Hz
We can substitute these values into the formula to find the length, L:
\[ L = \frac{340}{2 \times 134} \]
Calculating this, we get:
\[ L \approx 1.27 \, \text{meters} \]
To convert this length to centimeters, we can multiply by 100 since there are 100 centimeters in a meter:
\[ L \approx 1.27 \times 100 \, \text{cm} \]
Therefore, the approximate length of the shortest air column that will respond to a tuning fork of frequency 134 Hz is 127 cm.