A source of sound of frequency 450 cycles/sec is stationary but an observer is moving toward a source with 34 m/sec speed. If the speed of sound is 340 m/sec, then the apparent frequency will be

CONCEPT:

Doppler effect:

• If the source or the observer or both, move with respect to the medium, the frequency observed may be different from the frequency of the source. This apparent change in frequency of the wave due to the motion of the source or the observer is called the Doppler Effect.
• A sound wave or electromagnetic wave of known frequency is sent towards a moving object. Some part of the wave is reflected from the object and its frequency is detected by the monitoring station. This change in frequency is called the Doppler shift.
• The general expression for apparent frequency: Suppose observer (O) and source (S) are moving in the same direction along a line with velocities v_O and v_S respectively. The velocity of sound is v and velocity of medium is v_m, then apparent frequency observed by the observer is given by

\(n' = \left[ {\frac{{\left( {v - {v_m}} \right) - {v_o}\;}}{{\left( {v + {v_m}} \right) - {v_s}}}} \right]{n^o}\)

Where n’= apparent frequency, n^o = natural frequency

CALCULATION:

Given – n_o = 450 cycles/sec, v = 340 m/sec and v_o = 34 m/sec

Formula to calculate the apparent frequency  when the observer is moving towards the source is

\(n' = \left[ {\frac{{v + {v_o}\;}}{v}} \right]{n^o}\)

\( \Rightarrow {n'} = \left[ {\frac{{340\; + \;34\;}}{{340}}} \right]450 = 495cycles/sec\)