Advertisements
Advertisements
प्रश्न
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.
Advertisements
उत्तर
Given:
Length of cylindrical metal tube L = 50 cm
Speed of sound in air v = 340 ms−1
Fundamental frequency \[\left( f_1 \right)\]of an open organ pipe :
\[f_1 = \left( \frac{v}{2L} \right)\]
\[ = \frac{340}{2 \times 50 \times {10}^{- 2}} = 340 \text { Hertz }\]
So, the required harmonics will be in the range of 1000 Hz to 2000 Hz.
\[f_2 = 2 \times 340 = 680 \text { Hz }\]
\[ f_3 = 3 \times 340 = 1020 \text{ Hz }\]
\[ f_4 = 4 \times 340 = 1360 \text{ Hz }\]
\[ f_5 = 5 \times 340 = 1700 \text { Hz }\]
\[ f_6 = 6 \times 340 = 2040 \text { Hz }\]
f2, f3, f4... are the second, third, fourth overtone, and so on.
The possible frequencies between 1000 Hz and 2000 Hz are 1020 Hz, 1360 Hz and 1700 Hz.
APPEARS IN
संबंधित प्रश्न
Which of the following is a mechanical wave?
Choose the correct option:
A standing wave is produced on a string clamped at one end and free at the other. The length of the string ______.
In a stationary wave,
(a) all the particles of the medium vibrate in phase
(b) all the antinodes vibrates in phase
(c) the alternate antinodes vibrate in phase
(d) all the particles between consecutive nodes vibrate in phase.
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?
The speed of sound in a medium depends on
A one-metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?
In Quincke's experiment the sound detected is changed from a maximum to a minimum when the sliding tube is moved through a distance of 2.50 cm. Find the frequency of sound if the speed of sound in air is 340 m s−1.
Find the fundamental, first overtone and second overtone frequencies of an open organ pipe of length 20 cm. Speed of sound in air is 340 ms−1.
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.
A 30.0-cm-long wire having a mass of 10.0 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 m s−1.
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.
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 bullet passes past a person at a speed of 220 m 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 m s−1.
Figure shows a person standing somewhere in between two identical tuning forks. each vibrating at 512 Hz. If both the tuning forks move towards right a speed of 5.5 m s−1, find the number of beats heard by the listener. Speed of sound in air = 330 m s−1.
A small source of sound vibrating at frequency 500 Hz is rotated in a circle of radius 100/π 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 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?
A metallic wire of 1 m length has a mass of 10 × 10−3 kg. If the tension of 100 N is applied to a wire, what is the speed of the transverse wave?
Change in temperature of the medium changes ______.
A spring breaks under tension of 10 kg wt.If the string is used to revolve a body of mass 1.2 kg in a horizontal circle. of radius 50 cm, what is the maximum speed with which a body can be revolved?
