Question

If the speed of sound in a medium is 340 m/s and a sound wave has a frequency of 680 Hz, what is its wavelength?

• A. 0.5 m
• B. 2 m
• C. 20 m
• D. 50 m

Answer 1

Answer:

A. 0.5 m

Fundamental Relationship of Sound Waves

• The speed (v), frequency (f), and wavelength (λ) of a wave are mathematically related by the formula: v = f × λ.
• To calculate the wavelength (λ), the formula is rearranged as: λ = v / f.

Calculation Steps

1. Given Data:
   • Speed of sound (v) = 340 m/s
   • Frequency (f) = 680 Hz
2. Calculation:
   • λ = 340 m/s / 680 Hz
   • λ = 0.5 meters

Key Concepts for Competitive Exams

• Wavelength (λ): Defined as the distance between two consecutive compressions or two consecutive rarefactions in a longitudinal wave.
• Frequency (f): The number of oscillations or cycles per unit time, measured in Hertz (Hz).
• Speed of Sound: This is determined by the medium's properties—specifically its elasticity (stiffness) and density. Sound travels fastest in solids, followed by liquids, and slowest in gases.
• Medium Dependency: The speed of sound remains constant in a specific medium at a constant temperature, regardless of the frequency or wavelength of the sound wave. If the frequency of a sound wave increases, its wavelength must decrease proportionally to keep the speed constant.