Sound crossing a boundary
Definition
Medium
A substance whose particles pass on the oscillations of a mechanical wave, such as sound, from one place to another.
- When sound crosses from one medium into another, its speed usually changes because particle spacing, stiffness and density affect how quickly vibrations are transferred.
- The source remains unchanged, so the frequency is unchanged at the boundary.
- The wavelength changes because v=fλv=f\lambdav=fλ.
Linking speed and wavelength
- If sound speed increases while frequency stays constant, wavelength increases.
- If sound speed decreases while frequency stays constant, wavelength decreases.
- The ratio is v2v1=λ2λ1\dfrac{v_2}{v_1}=\dfrac{\lambda_2}{\lambda_1}v1v2=λ1λ2 because fff is the same on both sides.
- The period T=1fT=\dfrac{1}{f}T=f1 also remains unchanged.
Direction and transmission
- Sound arriving at an angle may refract because one side of the wavefront changes speed first.
- If sound speeds up, it bends away from the normal; if it slows down, it bends towards the normal.
- Sound arriving along the normal changes speed and wavelength without changing direction.
- At the same boundary, some sound energy may be reflected and some may be absorbed, so the transmitted amplitude can be smaller.
Sound in different materials
- Sound generally travels faster in solids than in liquids and faster in liquids than in gases because the restoring forces between particles are stronger in more rigid media.
- Density alone is not a complete rule because wave speed depends on both density and stiffness.
- A change in wave speed does not mean the sound source has changed pitch because pitch is linked to frequency, which remains constant.
Example
Sound entering water
- A sound wave of frequency 500 Hz500\ \text{Hz}500 Hz travels at 340 m s−1340\ \text{m s}^{-1}340 m s−1 in air and 1500 m s−11500\ \text{m s}^{-1}1500 m s−1 in water.
- In air, λ1=340500=0.68 m\lambda_1=\dfrac{340}{500}=0.68\ \text{m}λ1=500340=0.68 m.
- In water, λ2=1500500=3.0 m\lambda_2=\dfrac{1500}{500}=3.0\ \text{m}λ2=5001500=3.0 m.
- The frequency stays at 500 Hz500\ \text{Hz}500 Hz while speed and wavelength both increase.
Exam technique
- For a three-quantity question, state each result explicitly: speed changes, frequency stays constant and wavelength changes in the same direction as speed.
- Support the relationship with v=fλv=f\lambdav=fλ and keep units consistent.
Common Mistake
- Do not state that frequency changes because the medium changes; the source sets frequency.
- Do not use density alone to predict sound speed because stiffness also affects the result.
Self review
- Which sound-wave quantity remains unchanged at a boundary?
- What happens to wavelength when sound speed increases?
- Why can sound refract when it enters a new medium at an angle?
- Why is density alone insufficient to predict sound speed?
- How are v2/v1v_2/v_1v2/v1 and λ2/λ1\lambda_2/\lambda_1λ2/λ1 related?
