A pipe that is open at both ends has a fundamental frequency of 330 Hz when the speed of sound in air is 333 m/s.

What is the length of this pipe? Answer in units of cm.

What is the second harmonic?

What is the third harmonic? Answer in units of Hz.

What is the fundamental frequency of this pipe when the speed of sound in air is increased to 363.9 m/s due to a rise in the temperature of the air? Answer in units of Hz.

To find the length of the pipe, we can use the formula for the fundamental frequency of an open pipe:

f = (v / 2L),

where f is the fundamental frequency, v is the speed of sound, and L is the length of the pipe.

Given that the fundamental frequency is 330 Hz and the speed of sound is 333 m/s, we can plug these values into the formula and solve for L:

330 = (333 / 2L).

Simplifying the equation, we get:

660L = 333.

Dividing both sides of the equation by 660, we find:

L = 0.505 m.

Since the answer needs to be in cm, we convert meters to centimeters:

L = 0.505 m * 100 cm/m = 50.5 cm.

Therefore, the length of the pipe is 50.5 cm.

The second harmonic occurs when the pipe vibrates at twice the frequency of the fundamental frequency. So, the second harmonic frequency is:

2 * 330 Hz = 660 Hz.

The third harmonic occurs when the pipe vibrates at three times the frequency of the fundamental frequency. So, the third harmonic frequency is:

3 * 330 Hz = 990 Hz.

Given that the speed of sound increases to 363.9 m/s, we can use the same formula as before to find the new fundamental frequency:

f' = (v' / 2L),

where f' is the new fundamental frequency, v' is the new speed of sound, and L is the length of the pipe.

Plugging in the values, we have:

f' = (363.9 / 2L).

Substituting the length L = 0.505 m, we get:

f' = (363.9 / 2 * 0.505).

Calculating the value, we find:

f' ≈ 361.38 Hz.

Therefore, the new fundamental frequency of the pipe when the speed of sound increases to 363.9 m/s is approximately 361.38 Hz.

To find the length of a pipe that is open at both ends, we can use the formula:

L = (v / 2f)

where L is the length of the pipe, v is the speed of sound in air, and f is the fundamental frequency.

For the given question, we are given the speed of sound in air (v = 333 m/s) and the fundamental frequency (f = 330 Hz).

Substituting these values in the formula, we have:

L = (333 m/s) / (2 * 330 Hz)
= 0.503 m

To convert this length to centimeters, we can use the conversion factor:
1 m = 100 cm

So, L = 0.503 m * 100 cm/m = 50.3 cm.

Therefore, the length of the pipe is 50.3 cm.

The second harmonic is the frequency at which the pipe vibrates with two complete wavelengths. In an open pipe, the second harmonic is twice the fundamental frequency.

So, the second harmonic for this pipe is 2 * 330 Hz = 660 Hz.

The third harmonic is the frequency at which the pipe vibrates with three complete wavelengths. In an open pipe, the third harmonic is three times the fundamental frequency.

So, the third harmonic for this pipe is 3 * 330 Hz = 990 Hz.

To find the fundamental frequency of the pipe when the speed of sound in air is increased to 363.9 m/s, we can use the same formula as before:

L = (v / 2f)

This time, we are given the speed of sound in air (v = 363.9 m/s), but we need to find the new fundamental frequency (f).

Rearranging the formula, we have:

f = v / (2L)

Substituting the known values, we have:

f = (363.9 m/s) / (2 * 0.503 m)
= 362.965 Hz

Therefore, the fundamental frequency of the pipe when the speed of sound increases to 363.9 m/s is approximately 362.965 Hz.

Note: In the calculations, some values have been rounded for simplicity, so the final answers may have a slight variation.

find lambda. Then the length of the pipe is lambda/2

hjkkhkj