The wavelength and frequency of a sound wave in medium A is 20 cm and 1650 Hz. Keeping the medium same, if wavelength is changed to 16 cm, then new frequency is

Options

A. 2060 Hz
B. 2062.5 Hz
C. 2061 Hz
D. 2063.0 Hz

Explanation

To find the new frequency of the sound wave when the wavelength is changed from 20 cm to 16 cm while keeping the medium the same, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between speed, frequency, and wavelength**:
The speed of a wave (v) is given by the formula:
\[ v = f \cdot \lambda \]
where \( f \) is the frequency and \( \lambda \) is the wavelength.

2. **Set up the equations for the two cases**:
For the first case (initial conditions):
\[ v_1 = f_1 \cdot \lambda_1 \]
For the second case (after changing the wavelength):
\[ v_2 = f_2 \cdot \lambda_2 \]
Here, \( f_1 = 1650 \, \text{Hz} \) and \( \lambda_1 = 20 \, \text{cm} \), and \( \lambda_2 = 16 \, \text{cm} \).

3. **Since the medium is the same, the speed of sound remains constant**:
Therefore, we can equate the two speeds:
\[ v_1 = v_2 \]
This gives us:
\[ f_1 \cdot \lambda_1 = f_2 \cdot \lambda_2 \]

4. **Rearranging the equation to find the new frequency**:
\[ f_2 = \frac{f_1 \cdot \lambda_1}{\lambda_2} \]

5. **Substituting the known values**:
\[ f_2 = \frac{1650 \, \text{Hz} \cdot 20 \, \text{cm}}{16 \, \text{cm}} \]

6. **Calculating the new frequency**:
- First, calculate the numerator:
\[ 1650 \cdot 20 = 33000 \]
- Now divide by the new wavelength:
\[ f_2 = \frac{33000}{16} = 2062.5 \, \text{Hz} \]

### Final Answer:
The new frequency \( f_2 \) is **2062.5 Hz**.