Consider the vehicle emitting sound wave of frequency 700 Hz moving towards an observer at a speed `22 m s^(-1)` . Assuming the observer to be at rest, and speed of sound to be `330 m s^(-1)` , the frequency of sound as measured by the observer is

Options

A. `(2525)/4 Hz`
B. `(1960)/3Hz`
C. `(2240)/3Hz`
D. `750 Hz`

Answer

To solve the problem of finding the frequency of sound as measured by an observer when a vehicle emitting sound is moving towards them, we can use the Doppler effect formula for sound waves. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Frequency of the sound emitted by the vehicle (N) = 700 Hz
- Speed of the vehicle (source) (VS) = 22 m/s
- Speed of sound in air (V) = 330 m/s

### Step 2: Write down the Doppler effect formula
When the source of sound is moving towards a stationary observer, the apparent frequency (N') can be calculated using the formula:
\[ N' = N \times \frac{V}{V - V_S} \]
where:
- \( N' \) = apparent frequency
- \( N \) = emitted frequency
- \( V \) = speed of sound
- \( V_S \) = speed of the source

### Step 3: Substitute the known values into the formula
Substituting the known values into the formula:
\[ N' = 700 \times \frac{330}{330 - 22} \]

### Step 4: Calculate the denominator
Calculate \( 330 - 22 \):
\[ 330 - 22 = 308 \]

### Step 5: Substitute the denominator back into the equation
Now, substituting back into the equation:
\[ N' = 700 \times \frac{330}{308} \]

### Step 6: Perform the division
Calculate \( \frac{330}{308} \):
\[ \frac{330}{308} \approx 1.0701 \]

### Step 7: Multiply by the emitted frequency
Now, multiply this result by 700:
\[ N' \approx 700 \times 1.0701 \approx 749.07 \]

### Step 8: Round off the result
Rounding off the result gives:
\[ N' \approx 750 \text{ Hz} \]

### Conclusion
Therefore, the frequency of sound as measured by the observer is approximately **750 Hz**.

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