$U_{i}=\frac{1}{2} k x^{2}$
$10=\frac{1}{2} k(0.3)^{2}$
$k=\frac{20}{0.09}$
The final potential energy of the spring is given as,
$U_{f}=\frac{1}{2} k x_{1}^{2}$
$=\frac{1}{2} \times \frac{20}{0.09}(0.45)^{2}$
$=22.5 \mathrm{J}$
The amount of work done is given as,
$W=U_{f}-U_{i}$
$=22.5-10$
$=12.5 \mathrm{J}$
Thus, the amount of work done is $12.5 \mathrm{J}$.
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Assume that the sound of the whistle is composed of components varying in frequency from $f_1=800 \mathrm{~Hz}$ to $f_2=1120 \mathrm{~Hz}$, as shown in the figure. The spread in the frequency (highest frequency - lowest frequency) is thus $320 \mathrm{~Hz}$. The speed of sound in still air is $340 \mathrm{~m} / \mathrm{s}$.
$1.$ The speed of sound of the whistle is
$(A)$ $340 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
$(B)$ $360 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $310 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
$(C)$ $310 \mathrm{~m} / \mathrm{s}$ for passengers in $A$ and $360 \mathrm{~m} / \mathrm{s}$ for passengers in $B$
$(D)$ $340 \mathrm{~m} / \mathrm{s}$ for passengers in both the trains
$2.$ The distribution of the sound intensity of the whistle as observed by the passengers in train $\mathrm{A}$ is best represented by
$Image$
$3.$ The spread of frequency as observed by the passengers in train $B$ is
$(A)$ $310 \mathrm{~Hz}$ $(B)$ $330 \mathrm{~Hz}$ $(C)$ $350 \mathrm{~Hz}$ $(D)$ $290 \mathrm{~Hz}$
Give the answer question $1,2$ and $3.$