Questions: Sound Waves and Longitudinal Propagation

Question 1

A bass note (low frequency, 80 Hz) and a treble note (high frequency, 4000 Hz) are played simultaneously from a speaker 100 meters away. Which arrives first?

• A. The treble note — higher frequency waves travel faster through air
• B. The bass note — lower frequency waves travel faster through air
• C. They arrive at the same time — sound speed in air depends on the medium, not frequency
• D. The treble note — shorter wavelength means the wave completes its journey in fewer cycles

Answer: (C)

Sound speed in air (~343 m/s at 20°C) is a property of the medium — its density and bulk modulus — not of the source's frequency. Both notes travel at the same speed and arrive simultaneously. Option D reflects a common confusion: shorter wavelength at the same speed means more oscillations per second (higher frequency), not faster travel. The relationship v = fλ shows that if v is fixed and f increases, λ decreases proportionally — the speed itself doesn't change.

Question 2

Sound travels about four times faster in water (~1480 m/s) than in air (~343 m/s), even though water is much denser. What explains this?

• A. Water molecules are more tightly packed, allowing direct physical contact transmission
• B. Water's bulk modulus (resistance to compression) is far higher than air's, and this effect dominates over its greater density
• C. Sound travels as a transverse wave in water, which propagates faster than the longitudinal mode in air
• D. Water's higher temperature at depth accelerates sound, raising the average speed

Answer: (B)

Sound speed v = √(B/ρ) depends on bulk modulus B (stiffness) and density ρ. Water has higher density than air (which would slow sound), but its bulk modulus is vastly higher — water resists compression far more strongly. The stiffness effect dominates: sound is transmitted so much more efficiently through water's strong intermolecular bonds that it travels ~4× faster despite the density penalty. Option C is wrong: sound is longitudinal in both water and air.

Question 3

A louder sound (greater amplitude) travels faster through the same medium than a quiet sound at the same frequency.

• T. True
• F. False

Answer: False

Amplitude measures the intensity of the pressure variation — how far above and below atmospheric pressure the compressions and rarefactions are. It determines loudness but has no effect on propagation speed. Speed depends only on medium properties (bulk modulus and density). A whisper and a shout in the same room travel at the same ~343 m/s. Students often assume a 'bigger' wave must move faster, but the restoring force and inertia of the medium are unchanged by amplitude.

Question 4

Sound waves require a medium to propagate because they depend on the physical displacement of particles in that medium.

• T. True
• F. False

Answer: True

Sound propagates by alternating compression and rarefaction of medium particles — each particle pushes its neighbor. Without particles, there is nothing to compress and rarefy. This is why sound cannot travel through a vacuum (light, an electromagnetic wave, can). The classic demonstration: a ringing bell inside an evacuated jar becomes inaudible as air is removed, even though the bell still vibrates. The mechanism is purely mechanical — particle displacement is the wave itself.

Question 5

Why does sound travel faster in warm air than in cold air, even though neither frequency nor amplitude has changed?

Model answer: Temperature increases the bulk modulus of air: warmer air has more energetically moving molecules that resist compression more elastically, effectively increasing the medium's stiffness. Since v = √(B/ρ) and bulk modulus increases with temperature while density slightly decreases (warmer air expands), both effects raise speed. In practice, sound speed in air increases by about 0.6 m/s per 1°C rise. Frequency and amplitude are properties of the source, not the medium — changing them doesn't change propagation speed.

This illustrates the key principle: sound speed is a property of the medium, not the source. Warm the medium and speed changes; change only the source (louder, higher pitch) and speed stays the same. The same principle explains why you hear thunder after seeing lightning: light arrives nearly instantly, but sound travels at a fixed medium-dependent speed, so the delay directly measures distance.