1800 waves are passing through a point in 2 minutes in a medium. What will be the wavelength if the speed of wave in the medium is 900 m/s ?

Answer

To solve the problem step by step, we need to find the wavelength of the wave given the number of waves passing through a point in a certain time and the speed of the wave in the medium.

### Step 1: Calculate the Frequency
We know that frequency (f) is defined as the number of waves passing a point per second.

Given:
- Number of waves = 1800
- Time = 2 minutes = 2 × 60 seconds = 120 seconds

Now, we can calculate the frequency using the formula:
\[ f = \frac{\text{Number of waves}}{\text{Time in seconds}} \]
Substituting the values:
\[ f = \frac{1800 \text{ waves}}{120 \text{ seconds}} \]
\[ f = 15 \text{ Hz} \]

### Step 2: Use the Wave Speed Formula
The speed (v) of a wave is related to its frequency (f) and wavelength (λ) by the formula:
\[ v = f \times \lambda \]

Given:
- Speed of the wave (v) = 900 m/s
- Frequency (f) = 15 Hz

### Step 3: Rearranging the Formula to Find Wavelength
We can rearrange the formula to solve for wavelength (λ):
\[ \lambda = \frac{v}{f} \]

### Step 4: Substitute the Values
Now, substitute the values of speed and frequency into the equation:
\[ \lambda = \frac{900 \text{ m/s}}{15 \text{ Hz}} \]
\[ \lambda = 60 \text{ m} \]

### Conclusion
The wavelength of the wave is **60 meters**.

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