[2 Mark Questions]

Question 12 Marks

Audible frequencies have a range of 20 Hz to 20,000 Hz. Express it in terms of wavelength in air.

Answer

Let the velocity of sound in air be $340 m / s$
Initial frequency $v _1=20 Hz$
Initial wavelength $\lambda_1=\frac{v}{V_1}$
$
=\frac{340}{20}=17 m
$
Final frequency $v _2=20 \times 10^3 Hz$
Final wavelength $\lambda_2=\frac{340}{20 \times 10^2}$
$
=17 \times 10^{-3}=0.017 m
$
The range of wavelength is from $17 m$ to $0.017 m$

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Question 22 Marks

Consider a source moving towards a listener at a speed of 0.9 v. Where v is the velocity of sound. Calculate the apparent frequency if the actual frequency is 600 Hz.

Answer

$\begin{aligned} \text { Apparent frequency, } n^{\prime} & =\left(\frac{v}{v-v_{ s }}\right) n \\ v_{ s }=0.9 v ; n & =600 Hz \text \\ n^{\prime} & =\left(\frac{v}{v-0.9 v}\right) 600=\left(\frac{v}{v(1-0.9)}\right) 600=\frac{1}{0.1} \times 600 \\ n^{\prime} & =6000 Hz \end{aligned}$

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Question 32 Marks

A wave of length $0.60$ cm is produced in air and travels with a velocity of $340\ ms^{-1}.$ Will it be audible to the human ear?

Answer

Wavelength, $\lambda=0.6 \times 10^{-2} m$
Velocity of sound, $v=340 ms ^{-1}$
Frequency, $n =\frac{v}{\lambda}$
$\Rightarrow n =\frac{340}{0.6 \times 10^{-2}} $
$\Rightarrow n =566.66 \times 10^2$
$\Rightarrow n =567 \times 10^2\ Hz .$

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