Question

A source producing a sound of frequency
500 Hz is moving towards a listener with a
velocity of 30 m
s-¹. The speed of the sound is
330 ms-¹. What will be the frequency heard
by listener?​

Answer 1

Answer:

Given:

Source is producing 500 Hz frequency sound and moving towards a stationary listener at a speed of 30 m/s

Speed of sound = 330 m/s

To find:

Apparent frequency heard by listener

Concept:

We have to apply Doppler's effect in this question. As the source moves towards the observer(listener) , the listener actually hears a higher frequency as compared to the actual frequency of sound from the source.

Calculation:

As per Doppler's effect relationship :

$\boxed{ \sf{ \bold{ \red{f_{app} = (\dfrac{v + v_{obs}}{v - v_{source}} ) \times f_{act} }}}}$

$\sf{ \implies \: f_{app} = (\dfrac{330 + 0}{330 - 30} ) \times 500}$

$\sf{ \implies \: f_{app} = (\dfrac{330}{300} ) \times 500}$

$\sf{ \implies \: f_{app} = (\dfrac{330}{3} ) \times 5}$

$\sf{ \implies \: f_{app} = (110 ) \times 5}$

$\sf{ \implies \: f_{app} = 550 \: hz}$

So final answer :

$\boxed{ \large{ \green{ \bold{ \sf{\: f_{app} = 550 \: hz}}}}}$

Answer 2

$\underline{\boxed{\mathfrak{ \huge{ \red{AnSwEr}}}}} \\ \\ \dagger \: \boxed{ \blue{ \rm{Given}}}$

A source producing a sound of frequency 500Hz is moving towards a listener with a velocitu of 30 m/s

The speed of the sound is 330 m/s

$\dagger \: \boxed{ \blue{ \rm{To \: Find}}}$

Apparent frequency heard by observer

$\dagger \: \boxed{ \blue{ \rm{Concept}}}$

As per Doppler's effect...

Source moves towards the listener so listener hears a higher frequency as compared to the actual frequency.

$\dagger \: \boxed{ \blue{ \rm{Formula}}}$

Apparent frequency heared by listener is given as....

$\: \: \: \: \: \: \: \: \: \: \: \underline{ \boxed{ \bold{ \pink{f{ \tiny{app}} = \frac{v + v{ \tiny{obs}}}{v - v{ \tiny{source}}} \times f{\tiny{act}}}}}}$

Here Vobs = 0

$\dagger \: \boxed{ \blue{ \rm{Calculation}}}$

$\leadsto \rm \: f{ \tiny{app}} = ( \frac{330}{330 - 30} ) \times 500 \\ \\ \leadsto \rm \: f{ \tiny{app}} = 1.1 \times 500 = 550 \: Hz \\ \\ \underline{ \boxed{ \orange{ \huge{ \rm{f{ \tiny{app}} = 550 \: Hz}}}}} \: \: \huge{ \red{ \star}}$