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.

see other post.

40cm

To determine the length of the air column that will respond to a tuning fork of frequency 140 Hz, we can use the formula:

n * λ = 2L

where:
n = the lowest possible harmonic (1 in this case, since the air column is closed at one end)
λ = wavelength of the sound wave
L = length of the air column

The wavelength can be calculated using the formula:

λ = v/f

where:
v = speed of sound in air (340 m/s)
f = frequency of the sound wave (140 Hz)

Plugging in the values:

λ = 340 m/s / 140 Hz
λ ≈ 2.43 m

Now, substituting this value of the wavelength into the first formula:

n * λ = 2L
1 * 2.43 m = 2L
L ≈ 1.22 m

Since the answer is required in centimeters, we can convert meters to centimeters by multiplying by 100:

L ≈ 1.22 m * 100 cm/m
L ≈ 122 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 122 cm.

To find the length of the shortest air column closed at one end that will respond to a tuning fork of a given frequency, we can use the formula:

L = (v / 4f) * (2n - 1)

Where:
L is the length of the air column
v is the speed of sound in air
f is the frequency of the tuning fork
n is an integer representing the harmonic number

In this case, the speed of sound in air is given as 340 m/s, and the frequency of the tuning fork is 140 Hz. We need to find the length of the air column when n is the smallest integer possible.

Let's substitute the given values into the formula:

L = (340 / (4 * 140)) * (2 * 1 - 1)

L = (340 / 560) * (2 - 1)

L = (0.6071) * (1)

L = 0.6071

Thus, the length of the shortest air column closed at one end that will respond to a tuning fork of frequency 140 Hz is approximately 0.6071 cm.