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?
Two waves represented by \[y = a\sin\left( \omega t - kx \right)\] and \[y = a\cos\left( \omega t - kx \right)\] \[y = a\cos\left( \omega t - kx \right)\] are superposed. The resultant wave will have an amplitude
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
A string of linear mass density 0⋅5 g cm−1 and a total length 30 cm is tied to a fixed wall at one end and to a frictionless ring at the other end (See figure). The ring can move on a vertical rod. A wave pulse is produced on the string which moves towards the ring at a speed of 20 cm s−1. The pulse is symmetric about its maximum which is located at a distance of 20 cm from the end joined to the ring. (a) Assuming that the wave is reflected from the ends without loss of energy, find the time taken by the string to region its shape. (b) The shape of the string changes periodically with time. Find this time period. (c) What is the tension in the string?
At a prayer meeting, the disciples sing JAI-RAM JAI-RAM. The sound amplified by a loudspeaker comes back after reflection from a building at a distance of 80 m from the meeting. What maximum time interval can be kept between one JAI-RAM and the next JAI-RAM so that the echo does not disturb a listener sitting in the meeting. Speed of sound in air is 320 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.
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?
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 Kundt's tube apparatus has a steel rod of length 1.0 m clamped at the centre. It is vibrated in its fundamental mode at a frequency of 2600 Hz. The lycopodium powder dispersed in the tube collects into heaps separated by 6.5 cm. Calculate the speed of sound in steel and in air.
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 train approaching a platform at a speed of 54 km h−1 sounds a whistle. An observer on the platform finds its frequency to be 1620 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 m s−1.
Two identical tuning forks vibrating at the same frequency 256 Hz are kept fixed at some distance apart. A listener runs between the forks at a speed of 3.0m 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 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.
Two submarines are approaching each other in a calm sea. The first submarine travels at a speed of 36 km h−1 and the other at 54 km 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 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 of the sound wave in water to be 1500 m s−1.
An operator sitting in his base camp sends a sound signal of frequency 400 Hz. The signal is reflected back from a car moving towards him. The frequency of the reflected sound is found to be 410 Hz. Find the speed of the car. Speed of sound in air = 324 m s−1
A source emitting sound at frequency 4000 Hz, is moving along the Y-axis with a speed of 22 m s−1. A listener is situated on the ground at the position (660 m, 0). Find the frequency of the sound received by the listener at the instant the source crosses the origin. Speed of sound in air = 330 m s−1.
Two sources of sound are separated by a distance of 4 m. They both emit sound with the same amplitude and frequency (330 Hz), but they are 180° out of phase. At what points between the two sources, will the sound intensity be maximum?
The speed of sound in hydrogen is 1270 m/s. The speed of sound in the mixture of oxygen and hydrogen in which they are mixed in 1:4 ratio is
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?
