I) A sound wave in air has a frequency of 265 Hz and travels with a speed of 343 m/s . How far apart are the wave crests (compressions)?

Verified step by step guidance

1. Identify the given values: frequency (f) = 265 Hz, speed of sound (v) = 343 m/s.
2. Recall the relationship between speed, frequency, and wavelength: \( v = f \lambda \), where \( \lambda \) is the wavelength.
3. Rearrange the formula to solve for wavelength (\( \lambda \)): \( \lambda = \frac{v}{f} \).
4. Substitute the given values into the rearranged formula: \( \lambda = \frac{343 \, \text{m/s}}{265 \, \text{Hz}} \).
5. Calculate the wavelength to find the distance between the wave crests, which is the wavelength of the sound wave.

Key Concepts

Wave Speed

Wave speed is the distance a wave travels per unit of time. It is calculated using the formula v = fλ, where v is the wave speed, f is the frequency, and λ (lambda) is the wavelength. In this context, the speed of sound in air is given as 343 m/s, which is essential for determining how far apart the wave crests are.

Frequency

Frequency refers to the number of cycles of a wave that pass a given point per second, measured in hertz (Hz). In this question, the frequency of the sound wave is 265 Hz, indicating that 265 wave cycles occur every second. This value is crucial for calculating the wavelength, which directly relates to the distance between wave crests.

Wavelength

Wavelength is the distance between successive crests (or compressions) of a wave. It can be calculated using the formula λ = v/f, where λ is the wavelength, v is the wave speed, and f is the frequency. For the given sound wave, calculating the wavelength will provide the distance between the wave crests, which is the answer to the question.