A source of sonic oscillation with frequency `n_0=600Hz` moves away and at right angles to a wall with velocity `u=30(m)/(s)`. A stationary reciever is located on the line of source in succession wall`rarr`source`rarr`receiver. If velocity of osund propagation is `v=330(m)/(s)`, then
Q. The wavelength of direct waves received by the receiver is

Options

A. (a)`50cm`
B. (b)`100cm`
C. (c)`150cm`
D. (d)`90cm`

Explanation

To solve the problem, we need to find the wavelength of the direct waves received by the receiver when a sonic source is moving away from a wall. Here are the steps to find the solution:

### Step 1: Identify the given values
- Frequency of the source, \( n_0 = 600 \, \text{Hz} \)
- Velocity of the source, \( u = 30 \, \text{m/s} \)
- Velocity of sound, \( v = 330 \, \text{m/s} \)

### Step 2: Calculate the frequency of the direct waves received by the receiver
The frequency of the direct waves (\( n_D \)) can be calculated using the formula:

\[ n_D = n_0 \cdot \frac{v}{v - u} \]

Substituting the values:

\[ n_D = 600 \cdot \frac{330}{330 - 30} \]

Calculating the denominator:

\[ 330 - 30 = 300 \]

Now substituting back into the equation:

\[ n_D = 600 \cdot \frac{330}{300} \]

### Step 3: Simplify the expression
We can simplify \( \frac{330}{300} \):

\[ \frac{330}{300} = 1.1 \]

Now, substituting this back into the frequency equation:

\[ n_D = 600 \cdot 1.1 = 660 \, \text{Hz} \]

### Step 4: Calculate the wavelength of the direct waves
The wavelength (\( \lambda \)) can be calculated using the formula:

\[ \lambda = \frac{v}{n_D} \]

Substituting the values:

\[ \lambda = \frac{330}{660} \]

### Step 5: Simplify to find the wavelength
Calculating the above expression:

\[ \lambda = 0.5 \, \text{m} \]

### Conclusion
The wavelength of the direct waves received by the receiver is \( 0.5 \, \text{m} \) or \( 50 \, \text{cm} \).

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