Two sinusoidal waves with same wavelengths and amplitudes travel in opposite directions along a string with a speed `10ms^-1`. If the minimum time interval between two instant when the string is flat is `0.5s`, the wavelength of the waves is

Options

A. 25 m
B. 20 m
C. 15 m
D. 10 m

Answer

To solve the problem, we need to find the wavelength of the two sinusoidal waves traveling in opposite directions along a string. Let's break down the solution step by step.

### Step 1: Understand the given information
We are given:
- Speed of the waves (v) = 10 m/s
- Minimum time interval (Δt) between two instances when the string is flat = 0.5 s

### Step 2: Determine the total time period (T)
The minimum time interval between two instances when the string is flat corresponds to half of the time period of the wave. This is because the string becomes flat (i.e., has zero displacement) at two points in one complete cycle of the wave.

Thus, we can express the time period (T) as:
\[ T = 2 \times \Delta t \]
Substituting the value of Δt:
\[ T = 2 \times 0.5 \, \text{s} = 1 \, \text{s} \]

### Step 3: Use the wave speed formula to find the wavelength (λ)
The relationship between wave speed (v), wavelength (λ), and time period (T) is given by the formula:
\[ v = \frac{\lambda}{T} \]
Rearranging this formula to find the wavelength gives:
\[ \lambda = v \times T \]

### Step 4: Substitute the known values
Now we can substitute the values of v and T into the equation:
\[ \lambda = 10 \, \text{m/s} \times 1 \, \text{s} = 10 \, \text{m} \]

### Conclusion
The wavelength of the waves is:
\[ \lambda = 10 \, \text{meters} \]

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