IP Combined Science Notes (Lower Sec, Year 1-2): 09) Waves, Light & Sound

Wave behaviour explains ripples on water, colour from prisms, and the pitch of your voice. Work with both qualitative diagrams and quantitative calculations.

Learning targets

• Define transverse and longitudinal waves with particle motion diagrams.
• Apply \( v = f\lambda \) to calculate wave speed, frequency, or wavelength.
• Draw ray diagrams for reflection, refraction, and dispersion.
• Interpret sound intensity and frequency data, including oscilloscope traces.

1. Wave terminology

Transverse waves: particles oscillate perpendicular to wave direction (light, water surface). Longitudinal waves: particles oscillate parallel to wave direction (sound).

2. Wave calculations

Worked example — Ripple tank

Ripples have wavelength \( \pu{1.5 cm} \) and frequency \( \pu{12 Hz} \).

\[ v = f\lambda = 12 \times 1.5 \times 10^{-2} = 0.18 , \pu{m.s-1}. \]

If wave speed remains constant and frequency doubles, wavelength halves.

Sound travel time

Speed of sound in air \( \approx \pu{340 m.s-1} \). Lightning thunder delay of \( \pu{4.5 s} \) implies distance:

\[ d = vt = 340 \times 4.5 = 1.53 \times 10^{3} , \pu{m}. \]

3. Light behaviour

Reflection

Law of reflection: angle of incidence = angle of reflection. Use normal line for diagrams.

Refraction

When light enters denser medium (higher refractive index), it bends towards the normal; speed decreases.

Snell's law for extension: \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \).

Dispersion

Prism splits white light into spectrum because different wavelengths refract at slightly different angles.

Worked example — Glass block experiment

Light enters glass at \( \theta_1 = \pu{35 ^\circ} \), refractive index \( n = 1.52 \).

\[ \sin \theta_2 = \frac{\sin 35^\circ}{1.52} = 0.376 \Rightarrow \theta_2 = \pu{22.1 ^\circ}. \]

Draw emergent ray parallel to incident ray when exiting a rectangular block (due to symmetrical refraction).

4. Sound wave interpretation

Oscilloscope trace amplitude corresponds to loudness; frequency determines pitch.

• Doubling amplitude doubles energy carried, approximate 6 dB increase.
• Higher frequency waves have shorter periods: \( T = \frac{1}{f} \).

Worked example — Frequency from oscilloscope

If \( \pu{4} \) divisions represent one full cycle and time-base setting is \( \pu{2.0 ms.div-1} \):

\[ T = 4 \times 2.0 \times 10^{-3} = 8.0 \times 10^{-3} , \pu{s}. \]

\[ f = \frac{1}{T} = 125 , \pu{Hz}. \]

Try it yourself

1. Sketch particle displacement diagrams comparing transverse and longitudinal waves.
2. A light ray passes from air into water at \( \pu{50 ^\circ} \) to the normal. Refractive index of water \( = 1.33 \). Calculate refracted angle and sketch the ray.
3. Two tuning forks produce beats at \( \pu{4 Hz} \). One fork has frequency \( \pu{256 Hz} \). Determine possible frequencies of the second fork and describe how to identify the higher one experimentally.

Wrap up with electricity at https://eclatinstitute.sg/blog/ip-combined-sciences-lower-sec-notes/IP-Combined-Science-Lower-Sec-10-Electricity-and-Magnetism-Essentials.