Advertisements
Advertisements
Question
A source emitting a sound of frequency v is placed at a large distance from an observer. The source starts moving towards the observer with a uniform acceleration a. Find the frequency heard by the observer corresponding to the wave emitted just after the source starts. The speed of sound in the medium is v.
Advertisements
Solution
Let d be the initial distance between the source and the observer.
If v is the speed of sound emitted by the observer, then the time taken by the sound to reach the observer is given by:
T1 = d/v
The source is also moving. Therefore, at t = T, it moves a distance of (s) and is given by :
\[s = 0 \times T + \frac{1}{2}a T^2\]
Time taken by the pulse to reach the observer :
\[\frac{\left( d - \frac{1}{2}a T^2 \right)}{v}\]
Time difference \[\left( ∆ t \right)\] between the two pulses :
\[\left( T + \left( \frac{d - \frac{1}{2}a T^2}{v} \right) \right) - \frac{d}{v}\]
\[T - \frac{a T^2}{2v}\]
On replacing u =\[\frac{1}{T}\],
the apparent frequency will be :
\[\frac{1}{∆ t}\] = \[\frac{2u v^2}{2uv - a}\]
APPEARS IN
RELATED QUESTIONS
Which of the following is a mechanical wave?
Two periodic waves of amplitudes A1 and A2 pass thorough a region. If A1 > A2, the difference in the maximum and minimum resultant amplitude possible is
The fundamental frequency of a string is proportional to
following Figure shows a wave pulse at t = 0. The pulse moves to the right with a speed of 10 cm s−1. Sketch the shape of the string at t = 1 s, 2 s and 3 s.
A wave is represented by the equation
\[y = \left( 0 \text{ cdot 001 mm }\right) \sin\left[ \left( 50 s^{- 1} \right)t + \left( 2 \cdot 0 m^{- 1} \right)x \right]\]
(a) The wave velocity = 100 m s−1.
(b) The wavelength = 2⋅0 m.
(c) The frequency = 25/π Hz.
(d) The amplitude = 0⋅001 mm.
A wave is described by the equation \[y = \left( 1 \cdot 0 mm \right) \sin \pi\left( \frac{x}{2 \cdot 0 cm} - \frac{t}{0 \cdot 01 s} \right) .\]
(a) Find the time period and the wavelength? (b) Write the equation for the velocity of the particles. Find the speed of the particle at x = 1⋅0 cm at time t = 0⋅01 s. (c) What are the speeds of the particles at x = 3⋅0 cm, 5⋅0 cm and 7⋅0 cm at t = 0⋅01 s?
(d) What are the speeds of the particles at x = 1⋅0 cm at t = 0⋅011, 0⋅012, and 0⋅013 s?
Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0 m from one of the speakers and 6.4 m from the other. If the sound signal is continuously varied from 500 Hz to 5000 Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air = 320 m s−1.
Two stereo speakers are separated by a distance of 2.40 m. A person stands at a distance of 3.20 m directly in front of one of the speakers as shown in figure. Find the frequencies in the audible range (20-2000 Hz) for which the listener will hear a minimum sound intensity. Speed of sound in air = 320 m s−1.
A cylindrical metal tube has a length of 50 cm and is open at both ends. Find the frequencies between 1000 Hz and 2000 Hz at which the air column in the tube can resonate. Speed of sound in air is 340 m s−1.
In a resonance column experiment, a tuning fork of frequency 400 Hz is used. The first resonance is observed when the air column has a length of 20.0 cm and the second resonance is observed when the air column has a length of 62.0 cm. (a) Find the speed of sound in air. (b) How much distance above the open end does the pressure node form?
An electronically driven loudspeaker is placed near the open end of a resonance column apparatus. The length of air column in the tube is 80 cm. The frequency of the loudspeaker can be varied between 20 Hz and 2 kHz. Find the frequencies at which the column will resonate. Speed of sound in air = 320 m s−1.
Two successive resonance frequencies in an open organ pipe are 1944 Hz and 2592 Hz. Find the length of the tube. The speed of sound in air is 324 ms−1.
A piston is fitted in a cylindrical tube of small cross section with the other end of the tube open. The tube resonates with a tuning fork of frequency 512 Hz. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of 32.0 cm. Calculate the speed of sound in the air of the tube.
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 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 m s−1.
The horn of a car emits sound with a dominant frequency of 2400 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 km h−1? Speed of sound in air = 340 m s−1.
A person riding a car moving at 72 km h−1 sound a whistle emitting a wave of frequency 1250 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 m s−1.
A bat emitting an ultrasonic wave of frequency 4.5 × 104 Hz flies at a speed of 6 m s−1between 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 m s−1.
Two trains are travelling towards each other both at a speed of 90 km h−1. If one of the trains sounds a whistle at 500 Hz, what will be the apparent frequency heard in the other train? Speed of sound in air = 350 m s−1.
A wave of frequency 500 Hz is traveling with a speed of 350 m/s. (a) What is the phase difference between two displacements at a certain point at times 1.0 ms apart? (b) what will be the smallest distance between two points which are 45° out of phase at an instant of time?
