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Question

The range of the frequency of audible sound is 20 Hz to 20 kHz. What is the range of wavelength for the audible sound at $$0^oC?$$ (Take velocity of sound as $$330 ms^{-1}$$ at $$0^oC$$)


A
Range=10.5m16.5mm
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B
Range=10.5m15.5mm
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C
Range=16.5m16.5mm
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D
Range=16.5m10.5mm
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Solution

The correct option is C $$Range=16.5m-16.5 mm$$
According to question, Temperature is constant and other surroundings are constant (gas,pressure etc...).
$$\implies$$ Formula for Velocity of Sound remain same i.e.,  $$v=u\lambda$$ , where  $$v$$  is the speed of sound,  $$u$$ is the frequency and  $$\lambda$$  is the wavelength of sound.
Velocity of Sound remains constant  i.e.,  $$v=330m/s$$  (# According to question given)
Range of Frequency$$(u)$$  given,  $$20- 20000$$ Hz
And,  $$\lambda = v/u$$
$$\implies$$ Range of  Wavelength$$(\lambda _R)$$ is,  $$330/20 - 330/20000\cong 16.5m - 16.5mm$$ 
$$\implies$$  $$Range  =  16.5m   -   16.5mm$$
Therefor, answer is option  C.

Physics

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