A resonating glass tube closed at one end is 4.0 cm wide and 47 cm long. What are the frequencies of the first three harmonics for the resonating tube? The speed of sound in air at this temperature is 346 m/s.

To calculate the frequencies of the harmonics for a resonating tube, we need to use the formula:

f = (n * v) / (2L)

where:
f = frequency of the harmonic
n = harmonic number (1, 2, 3, ...)
v = speed of sound in air
L = length of the tube

In this case, we are given:
L = 47 cm = 47/100 m (converting to meters)
v = 346 m/s

Let's calculate the frequencies of the first three harmonics:

For the first harmonic (n = 1):
f1 = (1 * 346) / (2 * 0.47)
= 346 / 0.94
≈ 368.09 Hz

For the second harmonic (n = 2):
f2 = (2 * 346) / (2 * 0.47)
= 692 / 0.94
≈ 735.96 Hz

For the third harmonic (n = 3):
f3 = (3 * 346) / (2 * 0.47)
= 1038 / 0.94
≈ 1105.32 Hz

Therefore, the frequencies of the first three harmonics for the resonating tube are approximately 368.09 Hz, 735.96 Hz, and 1105.32 Hz.

Please label the correct School Subject.

Sra

The fundamental or "first harmonic" wavelength is four times the pipe length. Review the integer rules for the other harmonics. The frequency is

(sound speed)/(wavelength)

bjhm