A 50cm long hollow glass cylinder is open at both ends and is suspended in air. A source o sound that produces a pure frequency is placed close to one end of the tube. The frequency of the sound is slowly increased from a very low value. The tube is first observed to resonate when the source frequency is 320Hz.
(I) The speed of the sound in the tube must be:
A: 320m/s
(II) The frequency of the source is slowly increased until resonance occurs again FOR THE THIRD TIME. The frequency at which this happens is:
(III) THe frequency when resonance occurs for the FIFTH time is:
open at both ends? the tube must be lambda/2 long
frequency*wavelength=velocitysound
320*2*.50=...
at the the the key to the second part is to realize the fundamental, the path is one wavelength (length of tube is half that). THe second harmonic, path must be two wavelength (tube is one wavelength), the third harmonic is when the path is three wavelengths (length)is 1.5 wavelength), fourth harmonic is when path is four wavlengths (length is 2.0 lambda), and so on
(I) To find the speed of sound in the tube, we need to know the mode of resonance that is occurring. In this case, the tube is open at both ends, so it will resonate at odd multiples of the fundamental frequency.
The fundamental frequency, also known as the first harmonic, is given by the formula:
f1 = v / (2L)
where f1 is the fundamental frequency, v is the speed of sound, and L is the length of the tube.
Given that the frequency at which resonance occurs is 320 Hz and the length of the tube is 50 cm (or 0.5 m), we can rearrange the formula to solve for the speed of sound:
v = 2L * f1
v = 2 * 0.5 * 320
v = 320 m/s
Therefore, the speed of the sound in the tube must be 320 m/s.
(II) To find the frequency at which resonance occurs for the third time, we need to find the third harmonic frequency. The third harmonic frequency is three times the fundamental frequency:
f3 = 3f1
= 3 * 320
= 960 Hz
Therefore, the frequency at which resonance occurs for the third time is 960 Hz.
(III) Similarly, to find the frequency at which resonance occurs for the fifth time, we need to find the fifth harmonic frequency. The fifth harmonic frequency is five times the fundamental frequency:
f5 = 5f1
= 5 * 320
= 1600 Hz
Therefore, the frequency at which resonance occurs for the fifth time is 1600 Hz.