A source of frequency 150 Hz is moving in the direction of a person with a velocity of 110 m / s . The frequency heard by the person will be (speed of sound in medium = 330 m / s )

Options

A. 225 Hz
B. 200 Hz
C. 150 Hz
D. 100 Hz

Answer

To solve the problem of finding the frequency heard by a person when a source of sound is moving towards them, we can use the Doppler effect formula. Here are the steps to solve the problem:

### Step 1: Identify the known values
- Frequency of the source (Fs) = 150 Hz
- Velocity of the source (Vs) = 110 m/s
- Velocity of sound in the medium (V) = 330 m/s

### Step 2: Write the Doppler effect formula for a source moving towards a stationary observer
The formula for the apparent frequency (F0) when the source is moving towards the observer is given by:
\[ F_0 = \frac{V}{V - V_s} \times F_s \]

### Step 3: Substitute the known values into the formula
Now, substituting the values into the formula:
\[ F_0 = \frac{330 \, \text{m/s}}{330 \, \text{m/s} - 110 \, \text{m/s}} \times 150 \, \text{Hz} \]

### Step 4: Simplify the denominator
Calculate the denominator:
\[ 330 \, \text{m/s} - 110 \, \text{m/s} = 220 \, \text{m/s} \]

### Step 5: Substitute back into the formula
Now substituting back into the formula:
\[ F_0 = \frac{330}{220} \times 150 \]

### Step 6: Calculate the fraction
Calculate \( \frac{330}{220} \):
\[ \frac{330}{220} = 1.5 \]

### Step 7: Multiply by the source frequency
Now multiply by the source frequency:
\[ F_0 = 1.5 \times 150 \, \text{Hz} = 225 \, \text{Hz} \]

### Step 8: Final answer
Thus, the frequency heard by the person is:
\[ F_0 = 225 \, \text{Hz} \]

### Summary
The frequency heard by the person is 225 Hz.

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