The speed of a wave in a medium is 760 m/s. If 3600 waves are passing through a point in the medium in 2 min, then their wavelength is

Options

A. 13.8 m
B. 25.3 m
C. 41.5 m
D. 57.2 m

Answer

To find the wavelength of a wave in a medium where the speed of the wave is given, we can follow these steps:

### Step 1: Determine the frequency of the wave.
We know that 3600 waves pass through a point in 2 minutes. First, we need to convert the time from minutes to seconds.

\[ \text{Time in seconds} = 2 \text{ minutes} \times 60 \text{ seconds/minute} = 120 \text{ seconds} \]

Now, we can find the frequency (ν) using the formula:

\[ \nu = \frac{\text{Number of waves}}{\text{Time in seconds}} = \frac{3600 \text{ waves}}{120 \text{ seconds}} = 30 \text{ Hz} \]

### Step 2: Use the wave speed formula to find the wavelength.
The relationship between wave speed (v), wavelength (λ), and frequency (ν) is given by the formula:

\[ v = \lambda \cdot \nu \]

We can rearrange this formula to solve for the wavelength (λ):

\[ \lambda = \frac{v}{\nu} \]

### Step 3: Substitute the known values into the wavelength formula.
We know the speed of the wave (v) is 760 m/s and the frequency (ν) we calculated is 30 Hz. Now we can substitute these values into the equation:

\[ \lambda = \frac{760 \text{ m/s}}{30 \text{ Hz}} = \frac{760}{30} \text{ m} \]

### Step 4: Perform the division to find the wavelength.
Now we can calculate:

\[ \lambda = 25.33 \text{ m} \]

Thus, the wavelength of the wave in the medium is approximately **25.33 meters**.

### Summary of the Solution:
1. Convert time from minutes to seconds.
2. Calculate frequency using the number of waves and time.
3. Use the wave speed formula to find the wavelength.
4. Substitute the values and perform the calculation.

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