S

Measuring Acoustic Wavelength and

VelocityDiva, Tama & Hafiz

Introduction

Wave properties:

Wavelength (λ): parallel displacement in one cycle.

Amplitude (a): maximum perpendicular displacement.

Period (t): time taken for one cycle.

Frequency (f): cycles undergone per unit time.

Velocity (v): linear displacement per unit time.

Resonance principle

Every half a cycle, a wave reaches its amplitude.

When the amplitude of a sound wave makes

contact with a physical barrier (e.g. the inside of a

tube), it amplifies the sound’s intensity. This effect

is called resonance.

Hypothesis

The relationship between velocity, wavelength and frequency is defined as v = λf

By generating a sound wave with a constant frequency and finding its wavelength through the points of resonance, we might be able to find the speed of sound through a medium using a derivative of the above formula.

Materials

Biuret

Tuning forks (216 Hz, 288 Hz, 512 Hz)

Bucket

Retort stand

Procedure

1. Fill the biuret to the brim with tap water.

2. Tap the tuning fork on a hard surface and listen to its vibration as closely to the surface as possible.

3. Open the biuret and let the water flow out. When the water level reaches a point of resonance, the note should be momentarily amplified.

4. Rinse and repeat until no further resonance is heard.

Assuming that the sound wave experiences resonance every half a cycle,

l2 – l1 = λ/2

Where l = distance of a given resonance point from the surface.

Sources of error

Irregular water flow

External disturbances

Tuning fork vibration frequency not necessarily the same as the sound wave generated

Human error False positives Mistiming Zero error/parallax

Results

216 HzNo

distance from opening (cm)

Test 1 Test 2

1 10.2 6.0

2 12.3 9.5

3 15.0 12.6

4 17.1 16.5

5 22.2 20.2

6 23.1

7 24.6

l2 – l1 = 2.1 cm, 3.5 cmCalculated length: 4.2 cm, 7.0 cmMean result: 5.6 cmCalculated velocity: 12.096 ms-1

  Average difference: 3.0 cm, 3.1 cmAvg. calculated length: 6.0 cm, 6.2 cmMean result: 6.1 cmCalculated velocity: 13.176 ms-1

288 Hz

No

distance from opening (cm)

Test 1 Test 2

1 3.0 7.6

2 6.1 10.3

3 8.5 14.6

4 11.2 17.9

5 13.1 20.7

6 14.5 24.4

7 19.5 26.2

8 23.7

9 28.8

l2 – l1 = 3.1 cm, 2.7 cmCalculated length: 6.2 cm, 5.4 cmMean result: 5.8 cmCalculated velocity: 16.704 ms-1

  Average difference: 3.7 cm, 3.1 cmAvg. calculated length: 7.4 cm, 6.2 cmMean result: 6.8 cmCalculated velocity: 19.584 ms-1

512 Hz

No

distance from opening (cm)

Test 1 Test 2

1 5.9 16.6

2 10.5 22.3

3 13.0 28.7

4 15.0 31.6

5 21.0 34.0

6 23.0 43.7

7 26.0

8 28.3

l2 – l1 = 4.6 cm, 5.7 cmCalculated length: 9.2 cm, 11.4 cmMean result: 10.3 cmCalculated velocity: 52.736 ms-1

  Average difference: 3.2 cm, 5.4 cmAvg. calculated length: 6.4 cm, 10.8 cmMean result: 8.1 cmCalculated velocity: 41.472 ms-1

Observation

The values calculated were much lower than the

known speed of sound in air (334.2 m/s)

This might be due to the experiment method,

which depends on human hearing to take readings

and is therefore prone to human error.

Conclusion

Though the concept is sound, a more reliable method of measurement is required to achieve proper results.

Hence, this lab session is inconclusive.

References

Brian Arnold et al. International A/AS-Level Physics. London: Hodder Education, 2008.

“Sound Waves”. Rice University Web Services. Rice University, n.d.