Which equation could be rearranged to calculate the frequency of a wave?
A. wavelength = frequency/speed
B. frequency = wavelength/speed
C. wavelength = speed/frequency
D. frequency = speed $\times$ wavelength
Answer (1)
The equation wavelength = frequency speed can be rearranged to calculate the frequency of a wave. The rearranged equation is frequency = wavelength speed .
Explanation
Understanding the Problem We are given four equations relating wavelength, frequency, and speed of a wave, and we need to identify which equation can be rearranged to solve for frequency.
Analyzing Each Equation Let's analyze each equation:
wavelength = speed frequency Rearranging for frequency, we get: frequency = wavelength × speed
frequency = speed wavelength This equation is already solved for frequency, but it's not the correct relationship.
wavelength = frequency speed Rearranging for frequency, we get: frequency = wavelength speed
frequency = speed × wavelength This equation is already solved for frequency, but it's not the correct relationship.
Identifying the Correct Equation The correct relationship between wavelength, speed, and frequency is: wavelength = frequency speed . Rearranging this equation to solve for frequency gives us frequency = wavelength speed .
Examples
Understanding the relationship between wave speed, frequency, and wavelength is crucial in various fields. For instance, in music, the frequency of a sound wave determines the pitch we hear. If we know the speed of sound in air (approximately 343 meters per second) and the wavelength of a musical note, we can calculate its frequency. This calculation helps in designing musical instruments and understanding acoustics. Similarly, in telecommunications, the frequency of electromagnetic waves used to transmit data is related to its wavelength, which is important for designing antennas and optimizing signal transmission.
