What is the velocity if the wavelength is 1m and the frequency is 345Hz?
The Correct Answer and Explanation is:
To find the velocity of a wave when the wavelength and frequency are known, we can use the fundamental wave equation:
[
v = f \lambda
]
where:
- (v) is the velocity of the wave,
- (f) is the frequency,
- (\lambda) is the wavelength.
In this case, the wavelength (\lambda) is given as 1 meter, and the frequency (f) is given as 345 Hz.
Step-by-step Calculation:
- Substitute the values into the wave equation: [
v = 345 \, \text{Hz} \times 1 \, \text{m}
] - Perform the multiplication: [
v = 345 \, \text{m/s}
]
Thus, the velocity of the wave is 345 meters per second (m/s).
Explanation
The relationship between wavelength, frequency, and velocity is crucial in wave physics. The velocity of a wave is determined by how fast the wave oscillates (frequency) and the distance between successive peaks (wavelength).
Frequency is measured in hertz (Hz), which represents cycles per second. Thus, if a wave has a frequency of 345 Hz, it means that 345 cycles of the wave pass a given point in one second.
Wavelength, measured in meters, indicates the physical distance over which the wave’s shape repeats. In this scenario, a wavelength of 1 meter signifies that each complete wave occupies a distance of 1 meter in space.
The equation (v = f \lambda) showcases the direct relationship among these three quantities: as frequency increases, the wavelength typically decreases, maintaining a constant velocity for a given medium. For instance, sound waves traveling through air at a frequency of 345 Hz have a wavelength of 1 meter, allowing us to determine their propagation speed as 345 m/s.
This relationship is not only fundamental in physics but also practical in various applications, including acoustics, optics, and telecommunications, where understanding wave behavior is essential for effective design and analysis.