SATHEE: Wave Motion 5 Question 1

Wave Motion 5 Question 1

1. A small speaker delivers $2 W$ of audio output. At what distance from the speaker will one detect $120 d B$ intensity sound? [Take, reference intensity of sound as $10^{- 12} W / m^{2}$

(2019 Main, 12 April II)]

(a) $40 c m$

(b) $20 c m$

(d) $30 c m$

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Answer:

Correct Answer: 1. (a)

Solution:

Loudness of sound in decible is given by

$β = 10 \log_{10} (\frac{I}{I_{0}})$

where, $I$ = intensity of sound in $W / m^{2}$ ,

$I_{0} =$ reference intensity $(= 10^{- 12} W / m^{2})$ , chosen because it is near the lower limit of the human hearing range.

Here, $β = 120 d B$

So, we have $120 = 10 \log_{10} (\frac{I}{10^{- 12}})$

$\Rightarrow 12 = \log_{10} (\frac{I}{10^{- 12}})$

Taking antilog, we have

$\begin{aligned} \Rightarrow & 10^{12} & = \frac{I}{10^{- 12}} \\ \Rightarrow & I & = 1 W / m^{2} \end{aligned}$

This is the intensity of sound reaching the observer.

Now, intensity,

$I = \frac{P}{4 π r^{2}}$

where, $r =$ distance from source,

$P = power of output source.$

Here, $P = 2 W$ , we have

$1 = \frac{2}{4 π r^{2}} \Rightarrow r^{2} = \frac{1}{2 π} \Rightarrow r = \sqrt{\frac{1}{2 π}} m = 0.398 m \approx 40 c m$

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Wave Motion 5 Question 1

1. A small speaker delivers $2 W$ of audio output. At what distance from the speaker will one detect $120 d B$ intensity sound? [Take, reference intensity of sound as $10^{- 12} W / m^{2}$

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

Wave Motion 5 Question 1

1. A small speaker delivers 2W of audio output. At what distance from the speaker will one detect 120dB intensity sound? [Take, reference intensity of sound as 10−12W/m2

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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1. A small speaker delivers $2 W$ of audio output. At what distance from the speaker will one detect $120 d B$ intensity sound? [Take, reference intensity of sound as $10^{- 12} W / m^{2}$