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Physics 3 Marks Question

Waves · UP Board (UPMSP) STD 11 Science (UPMSP - English Medium). 3 questions.

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Question 13 Marks
 A train standing at the outer signal of a railway station blows a whistle of frequency $400 Hz$ still air. The train begins to move with a speed of $10 m s ^{-1}$ towards the platform. What is the frequency of the sound for an observer standing on the platform? (sound velocity in air = $\left.330 m s ^{-1}\right)$
Answer
$\text{v}_0=400\text{Hz}\ \ \ \ \ \ \ \text{v}_\text{s}=10\text{m/ s}$Velocity of sound in air $\text{v}_\text{a}=330\text{m/ s}$
Apparent frequency by observer standing on platform
$\text{v}'\frac{\text{v}_\text{a}}{(\text{v}_\text{a}-\text{v}_\text{s})}\text{v}_0=\frac{330\times400}{(330-10)}$
$\text{v}'=\frac{330\times400}{320}=\frac{825}{2}=412.4\text{Hz}$
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Question 23 Marks
A tuning fork A, marked 512Hz, produces 5 beats per second, where sounded with another unmarked tuning fork B. If B is loaded with wax the number of beats is again 5 per second. What is the frequency of the tuning fork B when not loaded?
Answer
When the prong of B is loaded with wax, its frequency becomes less than the original frequency.
If we assume that the original frequency of B is 507, then on loading its frequency will be less than 507. The beats between A and B will be more than 5.
If we assume that the original frequency of B is 517, then on loading its frequency will be less than 517. The beats between A and B may be equal to 5.
Hence the frequency of the tuning fork B when not loaded should be 517.
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Question 33 Marks
A steel wire has a length of $12m$ and a mass of $2.10kg$. What will be the speed of a transverse wave on this wire when a tension of $2.06 \times 10^4N$ is applied?
Answer
l = 12M (Total mass) =2.10kg$\text{m}=\frac{\text{M}}{\text{l}}=\frac{2.1}{12}\text{T}=2.06\times10^4\text{N}$
$\therefore\text{v}\sqrt{\frac{\text{T}}{\text{m}}}\sqrt{\frac{2.06\times10^4\times12}{2.10}}=\sqrt{\frac{1236\times10^4}{105}}$
$=\sqrt{11.77}\times10^2=3.43\times10^2$
$\text{v}=343.0\text{m/ s}$
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