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 $0^{o}C?$ (Take velocity of sound as $330m{s}^{-1}$ at $0^{o}C$)

• A. $Range=10.5m-16.5mm$
• B. $Range=10.5m-15.5mm$
• C. $Range=16.5m-16.5mm$
• D. $Range=16.5m-10.5mm$

Answer 1

The correct option is C $Range=16.5m-16.5mm$

According to question, Temperature is constant and other surroundings are constant (gas,pressure etc...).

$⟹$ 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$\left(u\right)$ given, $20-20000$ Hz

And, $\lambda =v/u$

$⟹$ Range of Wavelength$\left({\lambda }_R\right)$ is, $330/20-330/20000\cong 16.5m-16.5mm$

$⟹$ $Range=16.5m-16.5mm$

Therefor, answer is option C.