Which one among the following is true for the speed of sound in a given medium?
- (a)Speed of sound remains same at all frequencies
- (b)Speed of sound is faster at higher frequencies
- (c)Speed of sound is slower at higher frequencies
- (d)Speed of sound is slower at higher wavelengths
Answer
Why
Correct — A, the speed of sound remains the same at all frequencies. In a given medium (at fixed temperature and pressure) sound travels at a fixed speed regardless of frequency; changing the frequency changes the wavelength instead, since v = f λ with v constant.
Why the others are wrong
- (b)Faster at higher frequencies — Wrong — in an ideal non-dispersive medium the speed does not increase with frequency; only the wavelength shortens.
- (c)Slower at higher frequencies — Wrong — the speed is independent of frequency; it does not fall as frequency rises.
- (d)Slower at higher wavelengths — Wrong — speed does not depend on wavelength either; v stays fixed while f and λ trade off.
Concept
Sound speed in a medium is set by the medium's properties (elasticity and density), not by the source frequency: v = √(B/ρ) in a fluid. Since v = f λ, raising the frequency simply shortens the wavelength proportionally, keeping v constant — which is why music of all pitches reaches you together.
Hold v fixed for a given medium: frequency and wavelength are inversely related (v = f λ). If different frequencies travelled at different speeds, a distant band would sound jumbled.
Key facts
- In a given medium, the speed of sound is the same for all frequencies.
- v = f λ, so higher frequency means shorter wavelength.
- Sound speed depends on the medium (elasticity, density) and temperature.
- Sound travels fastest in solids, slower in liquids, slowest in gases.
Study next
Common traps
- Thinking higher-pitched sound travels faster.
- Confusing a change in wavelength with a change in speed.
Asked as how the speed of sound depends on frequency in a given medium.
Related PYQs
The refractive index of fused quartz is 1.46 and that of sapphire is 1.77. If vq is the speed of light in quartz and vs is the speed of light in sapphire, then which one of the following relationships is correct?
- (a) vq > vs
- (b) vs > vq
- (c) vs = vq
- (d) vs = vq/2
Answer(a) vq > vs
Companion sound-wave item (v = f λ / properties of sound) in a 2020 NDA GAT paper.
Practice
- practice — not a real PYQ
If the frequency of a sound wave in air is doubled, its speed
- (a)doubles
- (b)halves
- (c)stays the same
- (d)becomes zero
Answer(c) stays the same (the wavelength halves). - practice — not a real PYQ
The speed of sound is greatest in
- (a)vacuum
- (b)air
- (c)water
- (d)steel
Answer(d) steel (a solid).