A train approaching a platform at a speed of
Question: A train approaching a platform at a speed of $54 \mathrm{~km} \mathrm{~h}^{-1}$ sounds a whistle. An observer on the platform finds its frequency to be $1620 \mathrm{~Hz}$. the train passes the platform keeping the whistle on and without slowing down. What frequency will the observer hear after the train has crossed the platform? The speed of sound in air $=332 \mathrm{~m} \mathrm{~s}^{-1}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\operatorname{cosec}^{3} \frac{1}{x^{2}}$ Solution:...
Read More →A person riding a car moving at
Question: A person riding a car moving at $72 \mathrm{~km} \mathrm{~h}^{-1}$ sound a whistle emitting a wave of frequency $1250 \mathrm{~Hz}$. What frequency will be heard by another person standing on the road (a) in front of the car (b) behind the car? Speed of sound in air $=340 \mathrm{~m} \mathrm{} \mathrm{s}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{1+\cot x}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt[3]{\sin 2 x}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{\cos 3 x}$ Solution:...
Read More →The horn of a car emits sound with a dominant frequency
Question: The horn of a car emits sound with a dominant frequency of $2400 \mathrm{~Hz}$. What will be the apparent dominant frequency heard by a person standing on the road in front of the car if the car is approaching at $18.0 \mathrm{~km} \mathrm{~h}^{-1}$ ? Speed of sound in air $=340 \mathrm{~m} \mathrm{~s}^{-}$ 1 Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sec ^{3}\left(x^{2}+1\right)$ Solution:...
Read More →Solve this following
Question: Differentiate each of the following w.r.t. $x$ : $\cos ^{2} x^{3}$ Solution:...
Read More →A traffic policeman standing on a road sounds a whistle emitting
Question: A traffic policeman standing on a road sounds a whistle emitting the main frequency of $2.00 \mathrm{kHz}$. What could be the apparent frequency heard by a scooter-driver approaching the policeman at a speed of $36.0 \mathrm{~km} \mathrm{~h}^{-1}$ ? Speed of sound in air = $340 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{\frac{1+\sin x}{1-\sin x}}$ Solution:...
Read More →A tuning fork of frequency 256 Hz produces 4 beats per second
Question: A tuning fork of frequency $256 \mathrm{~Hz}$ produces 4 beats per second with a wire of length $25 \mathrm{~cm}$ vibrating in its fundamental mode. The beat frequency decreases when the length is slightly shortened. What could be the minimum length by which the wire we shortened so that it produces no beats with the tuning fork? Solution:...
Read More →A piano wire A vibrates at a fundamental frequency of
Question: A piano wire $A$ vibrates at a fundamental frequency of $600 \mathrm{~Hz}$. A second identical wire $B$ produces 6 beats per second with it when the tension in $A$ is slightly increased. Find the the ratio of the tension in $A$ to the tension in $B$. Solution:...
Read More →A tuning fork of unknown frequency makes 5
Question: A tuning fork of unknown frequency makes 5 beats per second with another tuning fork which can cause a closed organ pipe of length $40 \mathrm{~cm}$ to vibrate in its fundamental mode. The beat frequency decreases when the first tuning fork is slightly loaded with wax. Find its original frequency. The speed of sound in air is $320 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Calculate the frequency of beats produced
Question: Calculate the frequency of beats produced in air when two sources of sound are activated, one emitting a wavelength of 32 $\mathrm{cm}$ and the other of $32.2 \mathrm{~cm}$. The speed of sound in air is $350 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →A tuning fork produces 4 beats per second
Question: A tuning fork produces 4 beats per second with another tuning fork of frequency $256 \mathrm{~Hz}$. The first one is now loaded with a little wax and the beat frequency is found to increase to 6 per second. What was the original frequency of the tuning fork? Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{\frac{a^{2}-x^{2}}{a^{2}+x^{2}}}$ Solution:...
Read More →A source of sound with adjustable frequency produces
Question: A source of sound with adjustable frequency produces 2 beats per second with a tuning fork when its frequency is either 476 $\mathrm{Hz}$ of $480 \mathrm{~Hz}$. What is the frequency of the tuning fork? Solution:...
Read More →A Kundt's tube apparatus has a steel rod of length
Question: A Kundt's tube apparatus has a steel rod of length $1.0 \mathrm{~m}$ clamped at the centre. It is vibrated in its fundamental mode at a frequency of $2600 \mathrm{~Hz}$. The lycopodium powder dispersed in the tube collects into heaps separated by $6.5 \mathrm{~cm}$. Calculate the speed of sound in steel and in air. Solution:...
Read More →A Kundt's tube apparatus has a copper rod
Question: A Kundt's tube apparatus has a copper rod of length $1.0 \mathrm{~m}$ clamped at $25 \mathrm{~cm}$ from one of the ends. The tube contains air in which the speed of sound is $340 \mathrm{~m} \mathrm{~s}^{-1}$. The powder collects in heaps separated by a distance of $5.0 \mathrm{~cm}$. Find the speed of sound waves in copper. Solution:...
Read More →Solve this following
Question: Differentiate each of the following w.r.t. x: $\frac{1}{\left(x^{2}-3 x+5\right)^{3}}$ Solution:...
Read More →The fundamental frequency of a closed pipe
Question: The fundamental frequency of a closed pipe is $293 \mathrm{~Hz}$ when the air in it is a temperature of $20^{\circ} \mathrm{C}$. What will be its fundamental frequency when the temperature changes to $22^{\circ} \mathrm{C}$ ? Solution:...
Read More →Show that if the room temperature changes by
Question: Show that if the room temperature changes by a small amount from $T$ to $T+\Delta T$, the fundamental frequency of an organ pipe changes from $f$ to $f+\Delta f$, where $\frac{\Delta t}{f}=\frac{\Delta T}{2 T}$ Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\left(a x^{2}+b x+c\right)^{6}$ Solution:...
Read More →A 30.0-cm-long wire having a mass of 10.0 g
Question: A $30.0-\mathrm{cm}$-long wire having a mass of $10.0 \mathrm{~g}$ is fixed at the two ends and is vibrated in its fundamental mode. A $50.0$-cm-long closed organ pipe, placed with its open end near the wire, is set up into resonance in its fundamental mode by the vibrating wire. Find the tension in the wire. Speed of sound in air $=340 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →