If five waves pass through a point of a medium in 10 seconds. what is its frequency and time period?if its wavelength is 5 cm, calculate the wave speed.
The Correct Answer and Explanation is :
To solve the problem, we need to calculate the frequency, time period, and wave speed of the waves passing through a medium.
Given Information:
- Number of waves = 5
- Time taken = 10 seconds
- Wavelength (λ) = 5 cm
Calculations:
- Frequency (f):
Frequency is defined as the number of waves passing through a point in one second. We can calculate frequency using the formula: [
f = \frac{\text{Number of waves}}{\text{Time (s)}}
] Substituting the given values: [
f = \frac{5 \text{ waves}}{10 \text{ s}} = 0.5 \text{ Hz}
] - Time Period (T):
The time period is the reciprocal of frequency and represents the time taken for one complete wave to pass a point. It can be calculated using the formula: [
T = \frac{1}{f}
] Substituting the frequency we calculated: [
T = \frac{1}{0.5 \text{ Hz}} = 2 \text{ seconds}
] - Wave Speed (v):
The wave speed can be calculated using the formula: [
v = f \times \lambda
] Here, we need to ensure that the wavelength is in meters for consistency in SI units: [
\lambda = 5 \text{ cm} = 0.05 \text{ m}
] Now substituting the values of frequency and wavelength: [
v = 0.5 \text{ Hz} \times 0.05 \text{ m} = 0.025 \text{ m/s}
]
Summary of Results:
- Frequency (f): 0.5 Hz
- Time Period (T): 2 seconds
- Wave Speed (v): 0.025 m/s
Explanation:
The frequency of a wave indicates how often the wave oscillates per second. In this case, with 5 waves passing a point in 10 seconds, the frequency is calculated to be 0.5 Hz, meaning that every second, half a wave passes by. The time period, which is the time taken for one complete wave cycle, is determined to be 2 seconds, indicating a slower oscillation rate. The wave speed, derived from the frequency and wavelength, shows how fast the wave propagates through the medium. In this instance, the speed is relatively low at 0.025 m/s, reflecting the medium’s characteristics and the relatively large wavelength of 5 cm. Understanding these parameters is crucial in wave mechanics, as they help in analyzing the behavior of waves in different media.