Advertisements
Advertisements
Question
The equation of a simple harmonic progressive wave is given by, y = 5cosπ`[200t - x/150]`, where x and y are in cm and ‘t’ is in second. Then the velocity of the wave is ______.
Options
2 m/s
150 m/s
200 m/s
300 m/s
Advertisements
Solution
The equation of a simple harmonic progressive wave is given by, y = 5cosπ`[200t - x/150]`, where x and y are in cm and ‘t’ is in second. Then the velocity of the wave is 300 m/s.
Explanation:
y = 5cos`[200pit - pi/150x]`
y = Acos(ωt - Kx)
A = 5 cm
ω = 200π
2πf = 200π = 100 Hz
K = `pi/150 = (2pi)/lambda`
λ = 300 cm
V = fλ = `100 xx 300 xx 10^-2 = 300` m/s
APPEARS IN
RELATED QUESTIONS
Answer in brief:
What are harmonics and overtones?
Find the fundamental, first overtone, and second overtone frequencies of a pipe, open at both the ends, of length 25 cm if the speed of sound in air is 330 m/s.
The equation of simple harmonic progressive wave is, y = sin π/2 (4t/0.025 – x/0.25). Where all quantities are in the S.I. system. Find the amplitude, frequency, wavelength, and velocity of the wave.
An open organ pipe and a closed organ pipe have the frequency of their first overtone identical. The ratio of length of open pipe to that of closed pipe is ______.
At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork. the vibrating length of wire ______.
Two open pipes of different lengths and same diameter in which the air column vibrates with fundamental frequencies 'n1', and 'n2' respectively. When both pipes are joined to form a single pipe, its fundamental frequency will be ______.
In a fundamental mode the time required for the sound wave to reach upto the closed end of a pipe filled with air is 't' second. The frequency of vibration of air column is ________.
A tube closed at one end and containing air produces fundamental note of frequency 256 Hz. If the tube is open at both ends, the fundamental frequency will be ____________.
An organ pipe has a fundamental frequency of 120 Hz. Its fourth overtone is 600 Hz. Find the type of the pipe.
An air column, closed at one end and open at the other resonates with a tuning fork of frequency v, when its length is 45 cm, 99 cm and at two other lengths in between these values. The wavelength of sound in air column is ____________.
An open pipe of certain length produces fundamental frequency f1. A closed pipe of some other length produces fundamental .frequency f2. When the two are joined to form a longer close tube, its fundamental frequency will be ____________.
The fundamental frequency of sonometer wire increases by 9 Hz, if its tension is increased by 69%, keeping the length constant. The frequency of the wire is ______.
A pipe of length 85 cm is closed from one end. Find the number of possible natural oscillations of air colunm in the pipe whose frequencies lie below 1250 Hz. The velocity of sound in air is 340 m/s.
If we study the vibration of a pipe open at both ends, then which of the following statements is not true?
The equation of simple harmonic wave is given as y = 5sin `pi/2(100t - x)`, where 'x' and 'y' are in metre and time in second. The period of the wave is ______
If the length and diameter of a wire are decreased, then for the same tension the natural frequency of stretched wire will ______.
In melde's experiment, when the tension decreases by 0.009 kg-wt, the number of loops changes from 4 to 5. The initial tension is ______.
The closed and open organ pipes have same length. When they are vibrating simultaneously in first overtone, produce three beats. The length of open pipe is made `1/3` rd and closed pipe is made three times the original, the number of beats produced will be ______.
A pipe Pc closed at one end and point Po open at both ends are vibrating in the second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe Pc to that of pipe, Po is ______.
(Neglect end correction).
An open pipe is in resonance in its 2nd harmonic with tuning fork of frequency f1. Now, it is closed at one end. If the frequency of the tuning fork is increased slowly from f1, then again a resonance is obtained with a frequency f2. If in this case the pipe vibrates nth harmonic, then ______.
Two organ pipes are emitting their fundamental notes, when each closed at end, give 5 beats per sec. If their fundamental frequencies are 250 Hz and 255 Hz, then find the ratio of their lengths.
A sonometer wire is subjected to a certain tension. If the tension is increased four times and the length of wire is reduced to half the original value, how is frequency of vibrations altered?
