Question

A source is moving towards a stationary observer with some velocity.the frequency of sound herd is 4/3of it's original frequency.then velocity of source is? ​

Answer 1

Answer:

• The velocity of the source (v_s) is v / 4 (or) 82.5 m/s

Given:

1. Let the natural Frequency be " f₀ "
2. Apparent Frequency (f_a) = 4 / 3 f₀
3. Let the speed of the sound be " v "

Explanation:

$\rule{300}{1.5}$

From the formula we know,

$\bullet\;\underline{\boxed{\sf f_a=\Bigg\lgroup\dfrac{v}{v\;\pm\;v_s}\Bigg\rgroup\;f_0}}$

Here,

• f_a Denotes apparent Frequency
• f₀ Denotes Natural Frequency.
• v Denotes Speed of sound.
• v_s Denotes velocity of source.

Now,

$\displaystyle\Rightarrow\sf f_a=\Bigg\lgroup\dfrac{v}{v\;\pm\;v_s}\Bigg\rgroup\;f_0$

As the source is moving towards the observer,Then at the denominator there will be negative sign.

$\displaystyle\Rightarrow\sf f_a=\Bigg\lgroup\dfrac{v}{v\;-\;v_s}\Bigg\rgroup\;f_0$

Substituting the values and solving,

$\displaystyle\Rightarrow\sf \dfrac{4}{3}\;f_0=\Bigg\lgroup\dfrac{v}{v-v_s}\Bigg\rgroup\times f_0\\\\\\\Rightarrow\sf \dfrac{4}{3}=\Bigg\lgroup\dfrac{v}{v-v_s}\Bigg\rgroup\\\\\\\Rightarrow\sf 4\times (v-v_s)=3\times v\\\\\\\Rightarrow\sf 4\;v-4\;v_s=3\;v\\\\\\\Rightarrow\sf4\;v-3\;v=4\;v_s\\\\\\\Rightarrow\sf 4\;v_s =v\\\\\\\Rightarrow\sf v_s=\dfrac{v}{4}\\\\\\\Rightarrow\sf v_s=\dfrac{330}{4}\;\;\;\;\bigg(v=330\;m/s\bigg)\\\\\\\Rightarrow\sf v_s=82.5$

$\displaystyle\Rightarrow\large{\underline{\boxed{\red{\sf v_s = 82.5\;m/s}}}}$

∴ The velocity of the source (v_s) is v / 4 (or) 82.5 m/s.

$\rule{300}{1.5}$

Answer 2

Answer:

The velocity of source is 82.5 m/s.

Explanation:

Let the original frequency of the sound be '$f$', the frequency of sound heard be '$f'$'. And the velocity of sound be 'v'. And also the velocity of source be '$v_s$'

Given,

$f' = 4f/3$

We know that the apparent frequency of the sound is given by;

$f' = f(\frac{v}{v-v_s} )$

$\frac{4f}{3} = f(\frac{330}{330-v_s} )$   [As the velocity of sound in air v = 330 m/s]

$4(330-v_s) = 3 (330)$

$4(330) - 3(330) = 4v_s$

$330 = 4v_s$

$v_s = 82.5 m/s$

Therefore, the velocity of source is 82.5 m/s.

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