Part 1

A 3m long pipe is in a room where the temperature is 20 degrees C. What is the frequency of the first harmonic if the pipe is closed at one end?

Part 2
sound traveling in air at 23 degrees C enters a cold front where the air temp is 2 degrees C. If the sound frequency is 1500 Hz determine the wavelength in the colder air and in the warmer air, respectively.

Part 3
The speed of an ultrasonic sound of frequency 45KHz in air is 342 m/s what is the air temp?

You need to use the equation that relates sound speed in air to temperature.

There are many sites to help you with this, such as
http://www.sengpielaudio.com/calculator-speedsound.htm

3. Ultrasonic sound has the same speed as sound we can hear. A sound speed of 342 m/s requires T = 19 C.

Part 1:

To find the frequency of the first harmonic in a closed pipe, you can use the formula:

f = (v / 2L)

where f is the frequency, v is the speed of sound, and L is the length of the pipe. The speed of sound in air at 20 degrees Celsius is approximately 343 m/s.

First, convert the length of the pipe to meters:
L = 3 m

Substitute the values into the formula:
f = (343 / 2 * 3)
f ≈ 57.17 Hz

Therefore, the frequency of the first harmonic in a closed 3m long pipe at 20 degrees Celsius is approximately 57.17 Hz.

Part 2:
To find the wavelength of sound when it enters a different medium with a different temperature, you can use the formula:

λ = v / f

where λ is the wavelength, v is the speed of sound, and f is the frequency of the sound.

First, find the wavelength in air at 23 degrees Celsius:
v1 = 343 m/s (speed of sound in air at 23 degrees Celsius)
f = 1500 Hz

Substitute the values into the formula:
λ1 = 343 / 1500
λ1 ≈ 0.2287 m

The wavelength in air at 23 degrees Celsius is approximately 0.2287 m.

Next, find the wavelength in the cold air at 2 degrees Celsius:
v2 = 331 m/s (speed of sound in cold air at 2 degrees Celsius)
f = 1500 Hz

Substitute the values into the formula:
λ2 = 331 / 1500
λ2 ≈ 0.2207 m

The wavelength in the colder air at 2 degrees Celsius is approximately 0.2207 m.

Therefore, the wavelength in the colder air is approximately 0.2207 m and in the warmer air is approximately 0.2287 m.

Part 3:
To find the air temperature with the given information, you can use the formula:

v = λ * f

where v is the speed of sound, λ is the wavelength, and f is the frequency.

First, convert the frequency to Hz:
f = 45 kHz = 45,000 Hz

Substitute the values into the formula:
342 = λ * 45,000

Rearrange the formula to solve for wavelength (λ):
λ = 342 / 45,000
λ ≈ 0.0076 m

Next, use the formula to find the speed of sound in air at a particular temperature:

v = 331.5 + (0.6 * T)

where T is the temperature in degrees Celsius.

Substitute the known speed of sound (342 m/s) and the calculated wavelength (0.0076 m) into the formula:
342 = 331.5 + (0.6 * T)

Simplify and solve for T:
0.6 * T = 342 - 331.5
0.6 * T = 10.5
T ≈ 17.5 degrees Celsius

Therefore, the air temperature is approximately 17.5 degrees Celsius.