Advertisements
Advertisements
Question
The first overtone frequency of a closed organ pipe P1 is equal to the fundamental frequency of a open organ pipe P2. If the length of the pipe P1 is 30 cm, what will be the length of P2?
Advertisements
Solution
Given:
Length of closed organ pipe L1 = 30 cm
Length of open organ pipe L2 = ?
Let \[f_1\] and \[f_2\] be the frequencies of the closed and open organ pipes, respectively.
The first overtone frequency of a closed organ pipe P1 is given by
\[f_1 = \frac{3v}{4 L_1}\]
where v is the speed of sound in air.
On substituting the respective values, we get :
\[f_1 = \frac{3v}{4 \times 30}\]
Fundamental frequency of an open organ pipe is given by:
\[f_2 = \left( \frac{v}{2 L_2} \right)\]
As per the question,
\[f_1 = f_2 \]
\[ \left( \frac{3 \times v}{4 \times 30} \right) = \left( \frac{v}{2 L_2} \right)\]
\[ \Rightarrow L_2 = 20 \text { cm }\]
∴ The length of the pipe P2 will be 20 cm.
APPEARS IN
RELATED QUESTIONS
What is the smallest positive phase constant which is equivalent to 7⋅5 π?
A string clamped at both ends vibrates in its fundamental mode. Is there any position (except the ends) on the string which can be touched without disturbing the motion? What if the string vibrates in its first overtone?
The equation \[y = A \sin^2 \left( kx - \omega t \right)\]
represents a wave motion with
The voice of a person, who has inhaled helium, has a remarkably high pitch. Explain on the basis of resonant vibration of vocal cord filled with air and with helium.
The bulk modulus and the density of water are greater than those of air. With this much of information, we can say that velocity of sound in air
The fundamental frequency of a vibrating organ pipe is 200 Hz.
(a) The first overtone is 400 Hz.
(b) The first overtone may be 400 Hz.
(c) The first overtone may be 600 Hz.
(d) 600 Hz is an overtone.
A steel tube of length 1.00 m is struck at one end. A person with his ear closed to the other end hears the sound of the blow twice, one travelling through the body of the tube and the other through the air in the tube. Find the time gap between the two hearings. Use the table in the text for speeds of sound in various substances.
Two point sources of sound are kept at a separation of 10 cm. They vibrate in phase to produce waves of wavelength 5.0 cm. What would be the phase difference between the two waves arriving at a point 20 cm from one source (a) on the line joining the sources and (b) on the perpendicular bisector of the line joining the sources?
The length of the wire shown in figure between the pulley is 1⋅5 m and its mass is 12⋅0 g. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest.
The sound level at a point 5.0 m away from a point source is 40 dB. What will be the level at a point 50 m away from the source?
Sound with intensity larger than 120 dB appears pain full to a person. A small speaker delivers 2.0 W of audio output. How close can the person get to the speaker without hurting his ears?
If the sound level in a room is increased from 50 dB to 60 dB, by what factor is the pressure amplitude increased?
A uniform horizontal rod of length 40 cm and mass 1⋅2 kg is supported by two identical wires as shown in figure. Where should a mass of 4⋅8 kg be placed on the rod so that the same tuning fork may excite the wire on left into its fundamental vibrations and that on right into its first overtone? Take g = 10 m s−2.
Two speakers S1 and S2, driven by the same amplifier, are placed at y = 1.0 m and y = −1.0 m(See figure). The speakers vibrate in phase at 600 Hz. A man stands at a point on the X-axis at a very large distance from the origin and starts moving parallel to the Y-axis. The speed of sound in air is 330 m s−1. (a) At what angle θ will the intensity of sound drop to a minimum for the first time? (b) At what angle will he hear a maximum of sound intensity for the first time? (c) If he continues to walk along the line, how many more can he hear?
The fundamental frequency of a closed pipe is 293 Hz when the air in it is a temperature of 20°C. What will be its fundamental frequency when the temperature changes to 22°C?
A source of sound with adjustable frequency produces 2 beats per second with a tuning fork when its frequency is either 476 Hz of 480 Hz. What is the frequency of the tuning fork?
A cylindrical tube, open at both ends, has a fundamental frequency v. The tube is dipped vertically in water so that half of its length is inside the water. The new fundamental frequency is
A boy riding on his bike is going towards east at a speed of 4√2 m s−1. At a certain point he produces a sound pulse of frequency 1650 Hz that travels in air at a speed of 334 m s−1. A second boy stands on the ground 45° south of east from his. Find the frequency of the pulse as received by the second boy.
