IB Physics: Waves - Sound and Light

Sound and light are the two most accessible wave phenomena in our daily lives, yet they form the bedrock of sophisticated concepts in IB Physics. Understanding their nature—from the mechanical vibrations of sound to the electromagnetic undulations of light—is crucial for explaining phenomena ranging from musical instruments to the colors of a soap bubble.

Sound Waves: Mechanical Longitudinal Waves

A sound wave is a quintessential example of a longitudinal wave, where the particles of the medium oscillate parallel to the direction of energy transfer. This creates regions of compression (high pressure) and rarefaction (low pressure) that propagate through a material medium like air, water, or steel. The frequency ($f$) of a sound wave, measured in hertz (Hz), directly determines its perceived pitch. A higher frequency corresponds to a higher pitch. The human auditory range is typically from 20 Hz to 20,000 Hz.

The speed of sound is not constant; it depends heavily on the medium. In general, sound travels faster in solids than in liquids, and faster in liquids than in gases, because it relies on particle interactions. For example, in air at room temperature (20°C), the speed of sound is approximately 343 m/s, while in steel, it can exceed 5000 m/s. A key formula connecting wave speed ($v$), frequency ($f$), and wavelength ($\lambda$) is the universal wave equation: $v=f\lambda$.

A critical application of sound wave properties is the Doppler effect. This is the perceived change in frequency (and thus pitch) of a wave when there is relative motion between the source of the wave and the observer. You experience this when a siren's pitch seems to drop as an ambulance passes you. The observed frequency ($f^{\prime }$) can be calculated using: $$f^{\prime }=f\left(\frac{v\pm v_o}{v\mp v_s}\right)$$ where $f$ is the source frequency, $v$ is the speed of sound in the medium, $v_o$ is the speed of the observer, and $v_s$ is the speed of the source. The choice of plus or minus depends on whether the motion is toward or away from the other. A common worked example: A police car emitting a 1000 Hz siren moves at 30 m/s toward a stationary observer. With the speed of sound at 340 m/s, the observed frequency is $f^{\prime }=1000\left(\frac{340}{340-30}\right)\approx 1097$ Hz.

Light as an Electromagnetic Wave

Unlike sound, light is a transverse wave and does not require a material medium. It is part of the electromagnetic spectrum, a continuous range of waves all traveling at the speed of light ($c$) in a vacuum, which is exactly 299,792,458 m/s (approximately $3.00\times 10^8$ m/s). Light waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation.

The electromagnetic spectrum is ordered by frequency and wavelength. Radio waves have the longest wavelengths and lowest frequencies, followed by microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. Visible light occupies only a tiny sliver of this spectrum, from about 400 nm (violet) to 700 nm (red). The energy ($E$) of a photon of light is directly proportional to its frequency, as given by $E=hf$, where $h$ is Planck's constant. This explains why ultraviolet light can cause sunburn (high frequency, high energy) while radio waves do not.

Optical Phenomena as Evidence for Wave Nature

The wave model of light is powerfully demonstrated by interference and diffraction experiments, which are central to the IB syllabus.

Young's Double Slit Experiment provides clear evidence for wave interference. When monochromatic light passes through two narrow, closely spaced slits, it diffracts, and the wavefronts from each slit overlap. This produces an interference pattern of alternating bright and dark fringes on a screen. A bright fringe (constructive interference) occurs when the path difference between light from the two slits is an integer multiple of the wavelength: $n\lambda =d\sin \theta$, where $d$ is the slit separation and $\theta$ is the angle to the fringe. The fringe spacing ($\Delta y$) on a screen distance $L$ away is given by $\Delta y=\frac{\lambda L}{d}$. This experiment quantitatively confirms the wavelength of light.

Single Slit Diffraction occurs when light passes through a single slit wider than its wavelength. The light spreads out, forming a central bright fringe that is much wider than the others. The first minimum (dark fringe) in the pattern occurs when the path difference between light from the top and bottom of the slit is one wavelength. The condition is given by $b\sin \theta =\lambda$, where $b$ is the slit width. This phenomenon limits the resolution of optical instruments.

Thin Film Interference is the colorful effect seen in soap bubbles and oil slicks. It occurs when light reflects off the top and bottom surfaces of a thin film. The two reflected waves interfere. Whether the interference is constructive or destructive depends on the optical path difference (which accounts for the wavelength inside the film) and any phase change that occurs upon reflection. A phase change of $\pi$ (equivalent to a $\lambda /2$ path difference) happens when light reflects off a boundary with a higher refractive index. For a film of thickness $t$ and refractive index $n$, constructive interference for normal incidence is given by $2nt=(m+\frac{1}{2})\lambda$, where $m$ is an integer. This explains why different colors (wavelengths) are reinforced at different film thicknesses.

Common Pitfalls

1. Confusing Wave Types: A fundamental error is treating light as a longitudinal wave or sound as a transverse wave. Remember: sound needs a medium and is longitudinal; light is transverse and electromagnetic. This distinction is vital for understanding phenomena like polarization (which applies only to transverse waves).
2. Doppler Effect Sign Conventions: Students often get the signs wrong in the Doppler formula. A reliable method: if the source and observer are moving toward each other, the observed frequency increases. This means the numerator should increase or the denominator decrease. Always sketch the scenario.
3. Path Difference vs. Phase Difference: In interference problems, confusing the condition for constructive and destructive interference is common. Constructive interference requires a path difference of $n\lambda$ (or a phase difference of $2n\pi$). Destructive interference requires a path difference of $(n+\frac{1}{2})\lambda$ (or a phase difference of $(2n+1)\pi$). For thin films, you must add the extra $\lambda /2$ path difference for a reflection phase change.
4. Misapplying Formulas in Diffraction: Using the double-slit formula ($d\sin \theta =n\lambda$) for a single-slit minimum is incorrect. The single-slit condition for a minimum is $b\sin \theta =n\lambda$. Note that here $n=1,2,\mathrm{3...}$ for minima, not maxima, and $b$ is the single slit width, not a separation.

Summary

• Sound waves are longitudinal mechanical waves characterized by frequency (pitch) and amplitude (loudness); their speed is medium-dependent, and the Doppler effect describes frequency shifts due to relative motion.
• Light is a transverse electromagnetic wave that propagates at a constant speed in a vacuum ($c$); it is part of a broad spectrum classified by wavelength and frequency, with photon energy given by $E=hf$.
• The wave nature of light is conclusively demonstrated by interference and diffraction: Young's double slit produces an interference pattern, single slit diffraction shows wave spreading, and thin film interference explains colors based on path differences and phase changes.
• Mastery requires clear differentiation between wave types, careful application of sign conventions in the Doppler effect, and precise use of path difference conditions for different optical setups.