If speed of sound in air is 340 `m//s` and in water is 1480 `m//s`.If frequency of sound is 1000 kHz, then find wavelength in water

Options

A. 2.96 mm
B. 1.48mm
C. 0.74 mm
D. 1mm

Answer

To find the wavelength of sound in water given the speed of sound and frequency, we can use the formula:

\[ v = f \times \lambda \]

where:
- \( v \) is the speed of sound,
- \( f \) is the frequency,
- \( \lambda \) is the wavelength.

### Step-by-Step Solution:

1. **Identify the given values:**
- Speed of sound in water, \( v = 1480 \, m/s \)
- Frequency, \( f = 1000 \, kHz = 1000 \times 10^3 \, Hz = 1 \times 10^6 \, Hz \)

2. **Use the formula to find the wavelength:**
Rearranging the formula for wavelength, we have:
\[ \lambda = \frac{v}{f} \]

3. **Substitute the values into the equation:**
\[ \lambda = \frac{1480 \, m/s}{1 \times 10^6 \, Hz} \]

4. **Calculate the wavelength:**
\[ \lambda = \frac{1480}{1000000} \, m \]
\[ \lambda = 0.00148 \, m \]

5. **Convert the wavelength to millimeters:**
Since \( 1 \, m = 1000 \, mm \):
\[ \lambda = 0.00148 \, m \times 1000 \, mm/m = 1.48 \, mm \]

### Final Answer:
The wavelength in water is \( 1.48 \, mm \).

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