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 solve the problem step by step, we will follow these calculations:

### Step 1: Convert time from minutes to seconds
Given that the time is 2 minutes, we need to convert this into seconds for our calculations.
\[ t = 2 \text{ minutes} = 2 \times 60 = 120 \text{ seconds} \]

**Hint:** Remember that 1 minute is equal to 60 seconds.

### Step 2: Calculate the frequency of the waves
We know that frequency (n) is the number of waves passing through a point in a given time. Here, 3600 waves pass in 120 seconds.
\[ n = \frac{\text{Number of waves}}{\text{Time in seconds}} = \frac{3600}{120} = 30 \text{ Hz} \]

**Hint:** Frequency is calculated by dividing the total number of waves by the total time taken.

### Step 3: Use the wave speed formula
The relationship between wave speed (V), frequency (n), and wavelength (λ) is given by the equation:
\[ V = n \lambda \]
We can rearrange this to find the wavelength:
\[ \lambda = \frac{V}{n} \]

**Hint:** This formula shows how speed, frequency, and wavelength are interconnected.

### Step 4: Substitute the values into the wavelength formula
We know the speed of the wave (V) is 760 m/s and the frequency (n) we calculated is 30 Hz. Now we can find the wavelength (λ):
\[ \lambda = \frac{760 \text{ m/s}}{30 \text{ Hz}} = \frac{760}{30} \approx 25.33 \text{ m} \]

**Hint:** When substituting values, ensure that the units are consistent (meters per second for speed and Hertz for frequency).

### Step 5: Round the answer
The wavelength can be rounded to two decimal places:
\[ \lambda \approx 25.33 \text{ m} \]

**Hint:** Rounding is often necessary for clarity, especially in physical measurements.

### Final Answer
The wavelength of the wave is approximately **25.33 meters**.