Question

an air column at 25°c in a closed tube was sent into vibration by a vibrating tunning fork of frequency 512hz, calculate the velocity at 25°c and length of the closed tube at first resonance. take speed of sound in air to be 330m/s​

Answer 1

To calculate the velocity at 25°C and the length of the closed tube at first resonance, we can use the formula v=fλ, where v is the velocity of sound, f is the frequency of the tuning fork, and λ is the wavelength.

Step-by-step explanation:

To calculate the velocity at 25°C and the length of the closed tube at first resonance, we can use the formula v=fλ, where v is the velocity of sound, f is the frequency of the tuning fork, and λ is the wavelength.

First, we need to find the wavelength. Since the tube is closed at one end, the values of the wavelength that give resonance are given by λ=4L/n, where L is the length of the tube and n is the harmonic number (in this case, n=1 for first resonance).

The speed of sound in air is given as 330 m/s, and the frequency of the tuning fork is given as 512 Hz. Plugging these values into the formula, we can calculate the velocity and the length of the closed tube at first resonance.

Answer 2

Answer: To calculate the velocity of sound in the air column and the length of the closed tube at first resonance, we can use the formula for the fundamental frequency (first resonance) of a closed tube:

f = v / (2L)

where:

f = frequency of the tuning fork (512 Hz)

v = velocity of sound in air at 25°C (330 m/s)

L = length of the closed tube

We need to find both the velocity of sound (v) and the length of the closed tube (L). Let's start by calculating the velocity of sound in air at 25°C:

Step 1: Convert the temperature to Kelvin

T(K) = T(°C) + 273.15

T(K) = 25 + 273.15 = 298.15 K

Step 2: Use the formula for the velocity of sound in air at a given temperature:

v = 331.3 √(T(K)/273.15)

v = 331.3 √(298.15/273.15) ≈ 343.7 m/s

Now that we have the velocity of sound (v ≈ 343.7 m/s), we can calculate the length of the closed tube (L) at first resonance:

512 Hz = 343.7 m/s / (2L)

Step 3: Rearrange the formula to solve for L:

L = 343.7 m/s / (2 * 512 Hz)

L = 343.7 m/s / 1024 Hz ≈ 0.3359 meters or 33.59 cm

So, at first resonance, the length of the closed tube is approximately 33.59 cm, and the velocity of sound in the air column at 25°C is approximately 343.7 m/s.