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 reflected waves received by the receiver is

Options

A. (a)`120cm`
B. (b)`50cm`
C. (c)`90cm`
D. (d)`60cm`

Explanation

To solve the problem step by step, we will start by calculating the frequency of the reflected wave and then find the wavelength of that wave.

### Step 1: Calculate the frequency of the reflected wave (n_r)

The formula for the frequency of the reflected wave when the source is moving away from the wall is given by:

\[ n_r = n_0 \times \frac{v}{v + u} \]

Where:
- \( n_0 = 600 \, \text{Hz} \) (frequency of the source)
- \( v = 330 \, \text{m/s} \) (velocity of sound)
- \( u = 30 \, \text{m/s} \) (velocity of the source)

Substituting the values into the formula:

\[ n_r = 600 \times \frac{330}{330 + 30} \]

Calculating the denominator:

\[ 330 + 30 = 360 \]

Now substituting back into the equation:

\[ n_r = 600 \times \frac{330}{360} \]

Calculating the fraction:

\[ \frac{330}{360} = \frac{11}{12} \]

Now substituting this back:

\[ n_r = 600 \times \frac{11}{12} = 550 \, \text{Hz} \]

### Step 2: Calculate the wavelength of the reflected wave (λ)

The wavelength can be calculated using the formula:

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

Where:
- \( n_r = 550 \, \text{Hz} \)

Substituting the values into the formula:

\[ \lambda = \frac{330}{550} \]

Calculating the fraction:

\[ \lambda = \frac{3}{5} \, \text{m} \]

### Step 3: Convert the wavelength to centimeters

To convert the wavelength from meters to centimeters, we multiply by 100:

\[ \lambda = \frac{3}{5} \times 100 = 60 \, \text{cm} \]

### Final Answer

The wavelength of the reflected waves received by the receiver is **60 cm**.

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