A surfer floating beyond the breakers notes 12 waves per minute passing her position.
The correct answer and explanation is:
The number of waves passing a specific point in a given amount of time is known as the wave frequency. In this case, the surfer observes 12 waves per minute, meaning the frequency of waves is 12 waves/minute.
Wave Frequency:
The frequency (f) of a wave is defined as the number of wave cycles that pass a given point in one second. It is typically measured in Hertz (Hz), where 1 Hz equals 1 cycle per second. To convert the number of waves passing per minute into frequency in Hz, we need to divide by the number of seconds in a minute (60 seconds).
Thus, the frequency (in Hz) of the waves is calculated as: f=12 waves/minute60 seconds/minute=0.2 Hzf = \frac{12 \text{ waves/minute}}{60 \text{ seconds/minute}} = 0.2 \text{ Hz}
So the waves are passing at a rate of 0.2 cycles per second.
Additional Concepts:
- Wavelength: The wavelength (λ) is the distance between two consecutive crests (or troughs) of a wave. The wavelength is inversely related to frequency: as the frequency increases, the wavelength tends to decrease, and vice versa.
- Wave Speed: The wave speed (v) is the speed at which the wave propagates through the medium. Wave speed is related to frequency and wavelength by the formula:
v=f×λv = f \times \lambda
Where:
- vv is the speed of the wave,
- ff is the frequency of the wave,
- λ\lambda is the wavelength.
In this case, the surfer notices the number of waves but does not provide information about the wavelength or wave speed. To calculate the wave speed, more data would be needed, such as the distance between the wave crests.
Importance of Frequency:
Understanding the frequency of waves is important for surfers because it helps predict wave patterns and assess the difficulty of navigating through the waves. A higher frequency typically corresponds to smaller, more frequent waves, whereas a lower frequency is associated with larger, less frequent waves.