a pipe of length 1.00 m and open at both ends is lying on the ground at a construction site on a windy day of temperature 20 degrees C. Justin notices that the pipe is resonating and creating a sound of a particular frequency, the fundamental frequency.

a) what is this frequency?
b)just for fun, justin uses a board to close up one end of the pipe. the pipe now acts as a closed-tube resonator. what fundamental frequency does he now hear?

To calculate the frequency of the fundamental mode of vibration for a pipe that is open at both ends, we can use the formula:

f = v / (2L)

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

a) First, we need to find the speed of sound in air at 20 degrees Celsius. The speed of sound in air depends on temperature and can be calculated using the formula:

v = 331.4 + 0.6T

where T is the temperature in degrees Celsius.

Substituting T = 20 degrees Celsius, we get:

v = 331.4 + 0.6 * 20
v = 331.4 + 12
v = 343.4 m/s

Now, substituting the values into the formula, we can calculate the frequency:

f = 343.4 / (2 * 1.00)
f = 343.4 / 2
f = 171.7 Hz

Therefore, the frequency of the fundamental mode of vibration for the pipe open at both ends is 171.7 Hz.

b) When Justin closes one end of the pipe with a board, the pipe acts as a closed-tube resonator. For a closed-tube resonator, the fundamental frequency is given by:

f = v / (4L)

Using the same speed of sound in air (v = 343.4 m/s) and length of the pipe (L = 1.00 m), we can calculate the new fundamental frequency:

f = 343.4 / (4 * 1.00)
f = 343.4 / 4
f = 85.85 Hz

Therefore, the fundamental frequency Justin would hear when the pipe acts as a closed-tube resonator is approximately 85.85 Hz.

To find the fundamental frequency of the pipe lying on the ground, we can use the formula for the fundamental frequency of an open tube:

f = v / (2L)

where:
f = frequency
v = speed of sound
L = length of the pipe

For part a, we need to know the speed of sound at 20 degrees Celsius. The speed of sound in air can be approximated using the equation:

v = 331.5 + 0.6T

where T is the temperature in degrees Celsius.

Substituting T = 20 degrees Celsius into the formula, we get:

v = 331.5 + 0.6 * 20
v = 331.5 + 12
v = 343.5 m/s

Now, substituting v = 343.5 m/s and L = 1.00 m into the formula for an open tube, we get:

f = 343.5 / (2 * 1.00)
f = 343.5 / 2
f = 171.75 Hz

So, the frequency produced by the pipe in its fundamental mode is approximately 171.75 Hz.

For part b, when Justin closes one end of the pipe to make it act as a closed-tube resonator, we need to use a different formula. The fundamental frequency of a closed tube is given by:

f = v / (4L)

Using the same value for the speed of sound (v = 343.5 m/s) and the new length of the pipe (L = 1.00 m), we can calculate the new fundamental frequency:

f = 343.5 / (4 * 1.00)
f = 343.5 / 4
f = 85.875 Hz

So, when Justin closes one end of the pipe, he will hear a fundamental frequency of approximately 85.875 Hz.