The frequency of a tuning fork is 220 Hz and the velocity of sound in air is 330 m/s. When the tuning fork completes 80 vibrations, the distance travelled by the wave is

Options

A. 100 m
B. 120 m
C. 140 m
D. 160 m

Explanation

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the given information
- Frequency of the tuning fork (ν) = 220 Hz
- Velocity of sound in air (v) = 330 m/s
- Number of vibrations = 80

### Step 2: Use the wave equation to find the wavelength (λ)
The relationship between frequency (ν), velocity (v), and wavelength (λ) is given by the equation:
\[ v = ν \cdot λ \]
From this equation, we can express the wavelength (λ) as:
\[ λ = \frac{v}{ν} \]

### Step 3: Substitute the known values to calculate the wavelength
Substituting the values of v and ν into the equation:
\[ λ = \frac{330 \, \text{m/s}}{220 \, \text{Hz}} \]
Calculating this gives:
\[ λ = 1.5 \, \text{m} \]

### Step 4: Calculate the distance travelled by the wave for 80 vibrations
The distance travelled by the wave for a certain number of vibrations can be calculated using the formula:
\[ \text{Distance} = \text{Number of vibrations} \times λ \]
Substituting the values:
\[ \text{Distance} = 80 \times 1.5 \, \text{m} \]
Calculating this gives:
\[ \text{Distance} = 120 \, \text{m} \]

### Final Answer
The distance travelled by the wave when the tuning fork completes 80 vibrations is **120 meters**.

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