IGCSE Physics 0625: Effect of Wavelength and Gap Size on Diffraction of Sound

A large open-air stadium concert is held next to a quiet residential street. The stadium's boundary is a continuous solid wall, except for a single wide opening where sound can pass directly through to the street outside. The music reaching this opening contains low-frequency bass notes with a wavelength of about $2.0\text{ m}$ , and high-frequency treble notes with a wavelength of about $0.20\text{ m}$ . The opening itself is $2.5\text{ m}$ wide.

(a) State the condition, in terms of wavelength and gap width, needed for a wave to diffract strongly as it passes through a gap. [1]

(b) Using this condition, state and explain which of the two types of sound, the bass notes or the treble notes, diffracts more strongly through the opening, spreading out into a much wider area of the street beyond. [2]

(c) A sound engineer wants to redesign the opening so that the treble notes ALSO diffract strongly through it. State one change she could make to the width of the opening, and explain why this would achieve her aim. [2]

Part (a): Condition for strong diffraction

A wave is diffracted most strongly when the width of the gap it passes through is about the same size as its wavelength. If the gap is much wider than the wavelength, the wave mostly carries straight on with little spreading.

Part (b): Comparing the bass and treble notes

Compare each wavelength with the $2.5\text{ m}$ gap width:

$\text{bass: } \frac{\text{gap width}}{\text{wavelength}} = \frac{2.5\text{ m}}{2.0\text{ m}} = 1.25$

$\text{treble: } \frac{\text{gap width}}{\text{wavelength}} = \frac{2.5\text{ m}}{0.20\text{ m}} = 12.5$

The bass notes’ wavelength ( $2.0\text{ m}$ ) is close to the gap width ( $2.5\text{ m}$ ), so the ratio is close to $1$ . This is near the condition for strong diffraction from part (a). The treble notes’ wavelength ( $0.20\text{ m}$ ) is much smaller than the gap width, so the ratio is far from $1$ .

This means the bass notes diffract much more strongly, spreading widely into the street, while the treble notes mostly continue straight through the opening with little spreading.

Part (c): Redesigning the opening for the treble notes

To make the treble notes ( $\lambda = 0.20\text{ m}$ ) also diffract strongly, the gap width needs to be close to $0.20\text{ m}$ rather than $2.5\text{ m}$ .

The engineer should make the opening much narrower, close to $0.20\text{ m}$ wide. Narrowing the gap towards the treble wavelength satisfies the condition from part (a) (gap width $\approx$ wavelength) for the treble notes, so they would then diffract strongly and spread out into the street as well.

Final answers

(a) Strong diffraction occurs when the gap width $\approx$ wavelength
(b) The bass notes diffract more strongly, since their $2.0\text{ m}$ wavelength is much closer to the $2.5\text{ m}$ gap width than the treble notes’ $0.20\text{ m}$ wavelength is
(c) Narrow the opening to about $0.20\text{ m}$ wide, so the gap width matches the treble wavelength and satisfies the condition for strong diffraction