Which of the following statements are TRUE of the speed of sound? Identify all that apply.
The speed of a sound wave depends upon its frequency and its wavelength.
The correct answer and explanation is :
The statement “The speed of a sound wave depends upon its frequency and its wavelength” is FALSE.
Explanation:
The speed of sound in a given medium is determined by the medium’s properties, specifically its density and elasticity (or stiffness). It is independent of frequency and wavelength for a given medium.
The speed of sound, denoted as v, in a medium can be described by the formula:
[
v = \sqrt{\frac{B}{\rho}}
]
where:
- v is the speed of sound,
- B is the bulk modulus (which measures the stiffness of the medium),
- ρ is the density of the medium.
For example, in air, the speed of sound at room temperature is approximately 343 m/s. This speed can change if the medium changes (e.g., it is faster in water and even faster in solids), but it does not depend on the frequency or wavelength of the sound.
Frequency and Wavelength Relationship:
While frequency (the number of cycles per second) and wavelength (the distance between two consecutive compressions or rarefactions in a sound wave) are related by the equation:
[
v = f \lambda
]
where:
- v is the speed of sound,
- f is the frequency of the wave,
- λ is the wavelength,
this equation shows that the wavelength and frequency are inversely related for a given speed. That is, if the frequency increases, the wavelength decreases, and vice versa, but the speed of sound (v) remains constant for the medium. Thus, the speed of sound is not dependent on the frequency or the wavelength themselves.
Conclusion:
The speed of sound is determined by the medium’s properties (such as temperature, density, and elasticity), not by the frequency or wavelength of the sound wave.