Here, frequency of sound emitted by system, V0=800Hz Speed of sound in air = 330 m/s Frequency of source, v = 10 Hz Velocity of sound = 330 m/s. Find the apparent frequency heard b... Here, frequency of sound emitted by system, V0=800Hz Speed of sound in air = 330 m/s Frequency of source, v = 10 Hz Velocity of sound = 330 m/s. Find the apparent frequency heard by the observer in different conditions. Read more

Steps to Solve

1. Identify the Given Information

   The problem provides the following information:

   • Frequency of the source, $f_0 = 800 , \text{Hz}$
   • Velocity of sound in air, $v = 330 , \text{m/s}$
   • Velocity of the observer, $v_o = 10 , \text{m/s}$
   • Velocity of the source, $v_s = 500 , \text{Hz}$

2. Understand the Doppler Effect Formula

   For the Doppler effect when the observer is moving towards a stationary source and the source is moving away, the observed frequency $f$ is given by:

   $$ f = f_0 \cdot \frac{v + v_o}{v - v_s} $$

3. Substitute the Known Values

   Substitute the values into the formula:

   • Here, $v = 330 , \text{m/s}$
   • Since the observer is moving towards the source, we increase the velocity of the observer: $v_o = 10 , \text{m/s}$
   • The source is moving with $v_s = 500 , \text{Hz}$.

   Therefore, substituting into the equation we have:

   $$ f = 800 \cdot \frac{330 + 10}{330 - 500} $$

4. Calculate the Result

   First, simplify the numerator and denominator:

   $$ f = 800 \cdot \frac{340}{-170} $$

   Now calculate the fraction:

   $$ f = 800 \cdot -2 = -1600 , \text{Hz} $$

5. Interpret the Result

   Since frequency cannot be negative, the sign indicates that the observer is moving towards a sound source which results in a frequency increase from the observer's perspective.