The speed of a wave in a medium is `960 ms^(-1).` If 3600 waves are passing through a point in the medium in one minute then calculate the wavelength.

Answer

To solve the problem, we need to find the wavelength of a wave given its speed and the number of waves passing a point in a certain time. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Speed of the wave (v) = 960 m/s
- Number of waves passing through a point in one minute = 3600 waves

### Step 2: Convert the number of waves per minute to waves per second
To find the frequency (f), we need to convert the number of waves from per minute to per second:
\[ \text{Frequency (f)} = \frac{\text{Number of waves}}{\text{Time in seconds}} = \frac{3600 \text{ waves}}{60 \text{ seconds}} = 60 \text{ waves/second} \]

### Step 3: Use the wave speed formula
The relationship between wave speed (v), wavelength (λ), and frequency (f) is given by the formula:
\[ v = \lambda \times f \]
We can rearrange this formula to solve for wavelength (λ):
\[ \lambda = \frac{v}{f} \]

### Step 4: Substitute the known values into the formula
Now we can substitute the values of speed and frequency into the formula:
\[ \lambda = \frac{960 \text{ m/s}}{60 \text{ waves/s}} = 16 \text{ m} \]

### Step 5: State the final answer
The wavelength (λ) is 16 meters.

### Summary of the solution
The wavelength of the wave is 16 meters.

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