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A travelling wave passes a point of obse...

A travelling wave passes a point of observation. At this point, the time interval between successive crests is 0.2 seconds and

A

the wavelength is 5 m

B

the frequency is 5 Hz

C

the velocity of propagation is 5 m/s

D

the wavelength is 0.2 m

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will break down the information given and use relevant formulas to find the required frequency of the wave. ### Step 1: Understand the Given Information The problem states that the time interval between successive crests of the wave is 0.2 seconds. This time interval is also known as the period (T) of the wave. **Hint:** Remember that the period (T) is the time taken for one complete cycle of the wave, which in this case is the time between two successive crests. ### Step 2: Identify the Formula for Frequency The frequency (f) of a wave is related to its period (T) by the formula: \[ f = \frac{1}{T} \] **Hint:** Frequency is the number of cycles per second, and it is the inverse of the period. ### Step 3: Substitute the Given Period into the Formula We know from the problem that: \[ T = 0.2 \text{ seconds} \] Now, we can substitute this value into the frequency formula: \[ f = \frac{1}{0.2} \] **Hint:** Make sure to perform the division correctly to find the frequency. ### Step 4: Calculate the Frequency Now, calculate the frequency: \[ f = \frac{1}{0.2} = 5 \text{ Hz} \] **Hint:** Remember that Hertz (Hz) is the unit of frequency, representing cycles per second. ### Step 5: Conclusion The frequency of the wave is: \[ f = 5 \text{ Hz} \] **Hint:** Always double-check your calculations to ensure accuracy. ### Final Answer The frequency of the wave is **5 Hz**.
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