An operator sitting in his base camp sends a sound signal
Question: An operator sitting in his base camp sends a sound signal of frequency $400 \mathrm{~Hz}$. The signal is reflected back from a car moving towards him. The frequency of the reflected sound is found to be $410 \mathrm{~Hz}$. Find the speed of the car. Speed of sound in air $=324 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →A car moves with a speed of 54 km h-1 towards a cliff.
Question: A car moves with a speed of $54 \mathrm{~km} \mathrm{~h}^{-1}$ towards a cliff. The horn of the car emits sound of frequency $400 \mathrm{~Hz}$ at a speed of $335 \mathrm{~m} \mathrm{~s}^{-1}$. (a) Find the wavelength of the sound emitted by the horn in front of the car. (b) Find the wavelength of the wave reflected from the cliff. (c) What frequency does a person sitting in the car hear for the reflected sound wave? (d) How many beats does he hear in 10 seconds between the sound comin...
Read More →A person standing on a road sends a sound signal to the driver
Question: A person standing on a road sends a sound signal to the driver of a car going away from him at a speed of $72 \mathrm{~km} \mathrm{~h}^{-1}$. The signal travelling at $330 \mathrm{~m} \mathrm{~s}^{-1}$ in air and having a frequency of $1600 \mathrm{~Hz}$ gets reflected from the body of the car and returns. Find the frequency of the reflected signal as heard by the person. Solution:...
Read More →A boy riding on a bicycle going at
Question: A boy riding on a bicycle going at $12 \mathrm{~km} \mathrm{~h}^{-1}$ towards a vertical wall whistles at his dog on the ground. If the frequency of the whistle is $1600 \mathrm{~Hz}$ and the speed of sound in air is $330 \mathrm{~m} \mathrm{~s}^{-1}$, find (a) the frequency of the whistle as received by the wall (b) the frequency of the reflected whistle as received by the boy. Solution:...
Read More →A train running at 108 km h-1 towards east whistles at a dominant frequency
Question: A train running at $108 \mathrm{~km} \mathrm{~h}^{-1}$ towards east whistles at a dominant frequency of $500 \mathrm{~Hz}$. Speed of sound in air is $340 \mathrm{~m} / \mathrm{s}$. What frequency will a passenger sitting near the open window hear? (b) What frequency will a person standing near the track hear whom the train has just passed? (c) A wind starts blowing towards east at a speed of $36 \mathrm{~km} \mathrm{~h}^{-1}$. Calculate the frequencies heard by the passenger in the tra...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{\operatorname{cosec}\left(x^{3}+1\right)}$ Solution:...
Read More →A sound source, fixed at the origin,
Question: A sound source, fixed at the origin, is continuously emitting sound at a frequency of $660 \mathrm{~Hz}$. The sound travels in air at a speed of $330 \mathrm{~m} \mathrm{~s}^{-1}$. A listener is moving along the lien $x=336 \mathrm{~m}$ at a constant speed of $26 \mathrm{~m} \mathrm{~s}^{-1}$. Find the frequency of the sound as observed by the listener when he is (a) at $y=-140 \mathrm{~m}$, (b) at $y=0$ and (c) at $y=140 \mathrm{~m}$. Solution:...
Read More →A boy riding on his bike is going towards east at a speed of
Question: A boy riding on his bike is going towards east at a speed of $4 \sqrt{2} \mathrm{~m} \mathrm{~s}^{-1}$. At a certain point he produces a sound pulse of frequency $1650 \mathrm{~Hz}$ that travels in air at a speed of $334 \mathrm{~m} \mathrm{~s}^{-1}$. A second boy stands on the ground $45^{\circ}$ south of east from his. Find the frequency of the pulse as received by the second boy. Solution:...
Read More →A small source of sound oscillates in simple harmonic motion with
Question: A small source of sound oscillates in simple harmonic motion with an amplitude of $17 \mathrm{~cm}$. A detector is placed along the line of motion of the source. The source emits a sound of frequency $800 \mathrm{~Hz}$ which travels at a speed of $340 \mathrm{~m} \mathrm{~s}^{-1}$. If the width of the frequency band detected by the detector is $8 \mathrm{~Hz}$, find the time period of the source. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\cos (\sin \sqrt{a x+b})$ Solution:...
Read More →Two submarines are approaching each other in a calm sea.
Question: Two submarines are approaching each other in a calm sea. The first submarine travels at a speed of $36 \mathrm{~km} \mathrm{~h}^{-1}$ and the other at $54 \mathrm{~km} \mathrm{~h}^{-1}$ relative to the water. The first submarine sends a sound signal (sound waves in water are also called sonar) at a frequency of $2000 \mathrm{~Hz}$. (a) At what frequency is this signal received from the second submarine. At what frequency is this signal received by the first submarine. Take the speed of...
Read More →A car moving at 108 km h-1 finds another car in front it going
Question: A car moving at $108 \mathrm{~km} \mathrm{~h}^{-1}$ finds another car in front it going in the same direction at $72 \mathrm{~km} \mathrm{~h}^{-1}$. The first car sounds a horn that has a dominant frequency of $800 \mathrm{~Hz}$. What will be the apparent frequency heard by the driver in the front car? Speed of sound in air $=330 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\cot ^{3} x^{2}$ Solution:...
Read More →A traffic policeman sounds a whistle to stop a car-driver approaching towards him.
Question: A traffic policeman sounds a whistle to stop a car-driver approaching towards him. The car-driver does not stop and takes the plea in court that because of the Doppler shift, the frequency of the whistle reaching him might have gone beyond the audible limit of $25 \mathrm{kHz}$ and he did not hear it. Experiments showed that the whistle emits a sound with frequency closed to $16 \mathrm{kHz}$. Assuming that the claim of the driver is true, how fast was he driving the car? Take the spee...
Read More →Two trains are travelling towards each other both
Question: Two trains are travelling towards each other both at a speed of $90 \mathrm{~km} \mathrm{~h}^{-1}$. If one of the trains sounds a whistle at $500 \mathrm{~Hz}$, what will be the apparent frequency heard in the other train? Speed of sound in air $=350 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →A small source of sound vibrating at frequency
Question: A small source of sound vibrating at frequency $500 \mathrm{~Hz}$ is rotated in a circle of radius $100 / \pi \mathrm{cm}$ at a constant angular speed of $5.0$ revolutions per second. A listener situation situates himself in the plane of the circle. Find the minimum and the maximum frequency of the sound observed. 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. $x$ : $\sqrt{\cot \sqrt{x}}$ Solution:...
Read More →Figure shows a person standing somewhere in between
Question: Figure shows a person standing somewhere in between two identical tuning forks. each vibrating at $512 \mathrm{~Hz}$. If both the tuning forks move towards right a speed of $5.5 \mathrm{~m} \mathrm{~s}^{-1}$, find the number of beats heard by the listener. Speed of sound in air = $330 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{x \sin x}$ Solution:...
Read More →Two identical tuning forks vibrating at the same frequency
Question: Two identical tuning forks vibrating at the same frequency $256 \mathrm{~Hz}$ are kept fixed at some distance apart. A listener runs between the forks at a speed of $3.0 \mathrm{~m} \mathrm{~s}^{-1}$ so that he approaches one tuning fork and recedes from the other figure. Find the beat frequency observed by the listener. Speed of sound in air $=332 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →A violin player riding on a slow train plays
Question: A violin player riding on a slow train plays a $440 \mathrm{~Hz}$ note. Another violin player standing near the track plays the same note. When the two are closed by and the train approaches the person on the ground, he hears $4.0$ beats per second. The speed of sound in air $=340 \mathrm{~m} \mathrm{~s}^{-1}$. (a) Calculate the speed of the train. (b) What beat frequency is heard by the player in the train? Solution:...
Read More →Differentiate each of the following w.r.t.
Question: Differentiate each of the following w.r.t. $x$ : $\sqrt{\sin x^{3}}$ Solution: $\frac{d}{d x}(\sin x)=\cos x$...
Read More →Two electric trains run at the same speed of
Question: Two electric trains run at the same speed of $72 \mathrm{~km} \mathrm{~h}^{-1}$ along the same track and in the same direction with separation of $2.4$ $\mathrm{km}$ between them. The two trains simultaneously sound brief whistles. A person is situated at a perpendicular distance of $500 \mathrm{~m}$ from the track and is equidistant from the two trains at the instant of the whistling. If both the whistles were at $500 \mathrm{~Hz}$ and the speed of sound in air is $340 \mathrm{~m} \ma...
Read More →A bullet passes past a person at a speed of
Question: A bullet passes past a person at a speed of $220 \mathrm{~m} \mathrm{~s}^{-1}$. Find the fractional change in the frequency of the whistling sound heard by the person as the bullet crosses the person. Speed of sound in air $=330 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →A bat emitting an ultrasonic wave of frequency
Question: A bat emitting an ultrasonic wave of frequency $4.5 \times 10^{4} \mathrm{~Hz}$ flies at a speed of $6 \mathrm{~m} \mathrm{} \mathrm{s}^{-1}$ between two parallel walls. Find the fractional heard by the bat and the beat frequencies heard by the bat and the beat frequency between the two. The speed of sound is $330 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
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