The wave length of the sound produced by a source is 0.8m. If the source moves towards the stationary listener at `32 ms^(-1)` what is the apparent wave length of sound if the velocity of sound is `320 ms^(-1)`

Options

A. 0.32m
B. 0.4m
C. 0.72m
D. 0.80m

Answer

To find the apparent wavelength of sound when the source is moving towards a stationary listener, we can follow these steps:

### Step 1: Understand the given values
- Wavelength of the sound produced by the source (λ) = 0.8 m
- Speed of the source (Vs) = 32 m/s
- Velocity of sound in air (V) = 320 m/s

### Step 2: Use the formula for apparent wavelength
When the source of sound is moving towards a stationary observer, the apparent wavelength (λ') can be calculated using the formula:
\[ \lambda' = \frac{V - Vs}{V} \times \lambda \]
Where:
- λ' = apparent wavelength
- λ = actual wavelength
- V = velocity of sound
- Vs = speed of the source

### Step 3: Substitute the values into the formula
Now, substitute the known values into the formula:
\[ \lambda' = \frac{320 \, \text{m/s} - 32 \, \text{m/s}}{320 \, \text{m/s}} \times 0.8 \, \text{m} \]

### Step 4: Simplify the expression
Calculate the numerator:
\[ 320 - 32 = 288 \, \text{m/s} \]
Now substitute this back into the equation:
\[ \lambda' = \frac{288 \, \text{m/s}}{320 \, \text{m/s}} \times 0.8 \, \text{m} \]

### Step 5: Calculate the fraction
Now calculate the fraction:
\[ \frac{288}{320} = 0.9 \]

### Step 6: Calculate the apparent wavelength
Now multiply by the actual wavelength:
\[ \lambda' = 0.9 \times 0.8 \, \text{m} = 0.72 \, \text{m} \]

### Final Answer
The apparent wavelength of the sound heard by the stationary listener is **0.72 m**.

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