Answer
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Hint:In a given problem the angular speed of whistle is given. So, first calculate the linear velocity of the whistle by using the following expression.
${v_S} = r\omega $
Also the frequency of sound from the whistle is given and velocity of sound is also given.
According to the Doppler effect, if a source is moving then the frequency is given by the following expression of the observer.
${f_0} = \left( {\dfrac{v}{{v + {v_S}}}} \right){f_S}$
Where
${f_0} = $ Frequency heard by an observer
${f_S} = $ Frequency of source
$v = $ Velocity of sound
${v_S} = $ Velocity of source
So, on putting the values in above expression, we will get frequency of observer.
Complete step by step answer:
Given that angular velocity of source whistle is $\omega = 20$ rad per sec.
And the length of string $(\ell ) = 50cm$ this string revolves in a circle with a whistle.
So, $\ell = r = 50cm = 50 \times {10^{ - 2}}m$
So, linear velocity of source whistle is
$\Rightarrow {v_S} = r\omega = (50 \times {10^{ - 2}})(20)$
$\Rightarrow {v_S} = 1000 \times {10^{ - 2}}$
$\Rightarrow {v_S} = 10m/s$
According to Doppler effect, the frequency heard by observer is given by following expression
$\Rightarrow {f_0} = \left( {\dfrac{v}{{v + {v_S}}}} \right){f_S}$
Given that ${f_S} = 385Hz$
Velocity of sound $v = 340m/s$
$\Rightarrow {v_S} = 10m/s$
$\Rightarrow {f_0} = \left( {\dfrac{{340}}{{340 + 10}}} \right)385$
$\Rightarrow = \left( {\dfrac{{340}}{{350}}} \right)(385)$
$\Rightarrow = \dfrac{{34 \times 385}}{{35}}$
$\Rightarrow {f_0} = \dfrac{{13090}}{{35}}$
$\therefore {f_0} = 374Hz$
Hence, the maximum frequency heard by the observer is 374 Hz.
Note:
1. Observer Light source
Frequency $f' = \left( {1 + \dfrac{v}{c}} \right)f$
Wavelength $\lambda ' = \left( {1 - \dfrac{v}{c}} \right)\lambda $ Violet shift
2. Observer Light source
Frequency $f' = \left( {1 - \dfrac{v}{c}} \right)f$
Wavelength $\lambda ' = \left( {1 + \dfrac{v}{c}} \right)\lambda $ Red shift
${v_S} = r\omega $
Also the frequency of sound from the whistle is given and velocity of sound is also given.
According to the Doppler effect, if a source is moving then the frequency is given by the following expression of the observer.
${f_0} = \left( {\dfrac{v}{{v + {v_S}}}} \right){f_S}$
Where
${f_0} = $ Frequency heard by an observer
${f_S} = $ Frequency of source
$v = $ Velocity of sound
${v_S} = $ Velocity of source
So, on putting the values in above expression, we will get frequency of observer.
Complete step by step answer:
Given that angular velocity of source whistle is $\omega = 20$ rad per sec.
![seo images](https://www.vedantu.com/question-sets/c639f1a7-ce6f-4319-829c-a576aaba8b153805279479204136579.png)
And the length of string $(\ell ) = 50cm$ this string revolves in a circle with a whistle.
So, $\ell = r = 50cm = 50 \times {10^{ - 2}}m$
So, linear velocity of source whistle is
$\Rightarrow {v_S} = r\omega = (50 \times {10^{ - 2}})(20)$
$\Rightarrow {v_S} = 1000 \times {10^{ - 2}}$
$\Rightarrow {v_S} = 10m/s$
According to Doppler effect, the frequency heard by observer is given by following expression
$\Rightarrow {f_0} = \left( {\dfrac{v}{{v + {v_S}}}} \right){f_S}$
Given that ${f_S} = 385Hz$
Velocity of sound $v = 340m/s$
$\Rightarrow {v_S} = 10m/s$
$\Rightarrow {f_0} = \left( {\dfrac{{340}}{{340 + 10}}} \right)385$
$\Rightarrow = \left( {\dfrac{{340}}{{350}}} \right)(385)$
$\Rightarrow = \dfrac{{34 \times 385}}{{35}}$
$\Rightarrow {f_0} = \dfrac{{13090}}{{35}}$
$\therefore {f_0} = 374Hz$
Hence, the maximum frequency heard by the observer is 374 Hz.
Note:
1. Observer Light source
![seo images](https://www.vedantu.com/question-sets/413ac3c1-e109-4469-b007-0764d6c8d7472416577053793432873.png)
![seo images](https://www.vedantu.com/question-sets/d2209921-40d5-4f16-af3c-47afadd8f6088806010594086029194.png)
Frequency $f' = \left( {1 + \dfrac{v}{c}} \right)f$
Wavelength $\lambda ' = \left( {1 - \dfrac{v}{c}} \right)\lambda $ Violet shift
2. Observer Light source
![seo images](https://www.vedantu.com/question-sets/dc63cfbf-92dc-4382-99e6-0b8b9e3eec7c4251603397399438627.png)
![seo images](https://www.vedantu.com/question-sets/af201c49-e5b6-428e-ae30-9e7b10257c476221774534005107369.png)
Frequency $f' = \left( {1 - \dfrac{v}{c}} \right)f$
Wavelength $\lambda ' = \left( {1 + \dfrac{v}{c}} \right)\lambda $ Red shift
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