The wavelength of the sound emitted by a tuning fork in air is 3m. Speeds of sound in air and in water are 330 m/s and 1400 m/s respectively. Wavelength of this sound in water is

Options

A. 1m
B. 1.2 m
C. 110 m
D. 12.72 m

Answer

To find the wavelength of sound in water, we can follow these steps:

### Step 1: Understand the relationship between speed, frequency, and wavelength
The relationship between speed (v), frequency (f), and wavelength (λ) is given by the formula:
\[ v = f \cdot \lambda \]
This means that the speed of sound is equal to the product of its frequency and wavelength.

### Step 2: Calculate the frequency of sound in air
Given:
- Wavelength in air (λ_air) = 3 m
- Speed of sound in air (v_air) = 330 m/s

Using the formula:
\[ f = \frac{v}{\lambda} \]
We can calculate the frequency in air:
\[ f = \frac{330 \, \text{m/s}}{3 \, \text{m}} = 110 \, \text{Hz} \]

### Step 3: Use the frequency to find the wavelength in water
We know that the frequency remains constant when sound travels from air to water. Thus, the frequency in water (f_water) is also 110 Hz.

Given:
- Speed of sound in water (v_water) = 1400 m/s

We can now use the frequency to find the wavelength in water (λ_water):
\[ \lambda = \frac{v}{f} \]
Substituting the known values:
\[ \lambda_{water} = \frac{1400 \, \text{m/s}}{110 \, \text{Hz}} \]
Calculating this gives:
\[ \lambda_{water} \approx 12.73 \, \text{m} \]

### Final Answer
The wavelength of sound in water is approximately **12.73 m**.

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