Experiment 6

Exp 6
Speed of Sound

Purpose: To use fundamental frequency and spinning slinky to determine the speed of sound

Material:
Long, hollow, red plastic tube with one end closed
LoggerPro software
Measuring stick

Procedure:
Have the plastic tube spinning forming a circle. Use loggerpro software to measure the angular velocity, ω. Do the experiment several times to find several calculated values for velocity. 

v =λ f

(A.)

Frequency may be obtained by recalling that

ω = 2πf, giving 

f = ω/2π 

(B.)

While wavelength, λ, can be found by assuming that the wave pattern inside the tube would be harmonic wave:

(2n+1) λ/2 = L

 (C.)

whereas n is the number of harmonics and L length of pipe.

After λ and f were found, v, the speed of sound, can be calculated and compared.

Data and Uncertainty:

Length of pipe is 0.83 +/- 0.05 m

Two trials were conducted.

Trial 1:

ω = 3859 +/- 1 rad/s

f = 614 +/- 1 s^-1

Trial 2: 

ω = 5068 +/- 1 rad/s

f = 807 +/- 1 s^-1

The harmonics were found using the speed of sound, 340 m/s.

v = λf

v/f = λ

whereas from equation (C.), λ = 2L / (2n+1).

Both n's for trial 1 and 2 are 2+/- 0 and 3+/- 0, respectively (the uncertainty was 0 because if it were to be, for example, 2 +/- 0.05 carried from length, there is no such thing as 0.05 harmonics. Harmonics' value must be in integers).

n_1 = 2

n_2 = 3

From n, λ can be solved backwards,  using 

λ = 2L / (2n+1)

Trial 1:  λ = 0.56 +/- 0.05 m

Trial 2:  λ = 0.43 +/- 0.05 m

Putting the data together:

Trial 1: f = 614 +/- 1 s^-1, λ = 0.56 +/- 0.05 m

Velocity then, using equation (A.), is 343.84 +/- 1.05 m/s

Trial 2: f = 807 +/- 1 s^-1, λ = 0.43 +/- 0.05 m

v = 347.01 +/- 1.05 m/s

Whereas speed of sound at the sea level, according to https://www.google.com/, is 340.29 m/s

Although it does not fall within uncertainty values, the values were off by within less than 2.00% error, which can be considered insignificant. It was very close to the actual speed of sound.

Error Analysis:

Some of the possible rooms for error were the measurement of the length. The pipe had to be assumed initially to have constant diameter and did not deform when swung. Being a plastic pipe, some deformity must have occurred. This would alter the sound travel a little.

Second room for error was the rounding of harmonics, n. One value obtained was less than 3 (around 2.84, but it was rounded up to three). This altered the value by almost 10%.

END OF LAB 6.

Physics 4C complimentary guitar solo live performance