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Plane harmonic waves of frequency 500 Hz are produced in air with displacement amplitude 1 x 10^{3} cm. Deduce energy flux in J/m^{2}) in the wave (density of air =1.29 gm/lit, speed of sound in air = 340 m/s).
The correct answer is: 0.22
Plane harmonic waves of frequency 500 Hz are produced in air with displacement amplitude 1 x 10^{3} cm. Deduce pressure amplitude (in N/m^{2}). (density of air = 1.29 gm/lit, speed of sound in air = 340m/s)
Given A = 1 x 10^{3} cm = 10^{5} m, v = 500 Hz, v = 340 m/s, p = 1.29 g/lit = 1.29 kg/m^{3}
Pressure amplitude
= 2 x 3.14 x 10^{5} x 500 x 340 x 1.29
= 13.8 N/m^{2}
The correct answer is: 13.8
If the frequency of a tuning fork is 400 Hz and the velocity of sound in air is 320 m/s, find how far does the sound travel (in m) while the fork completes 30 vibrations?
∴ Distance travelled by the wave when the fork completes 1 vibration = 0.8 m.
So distance travelled by the wave when the fork completes 30 vibrations.
= 0.8 x 30
= 24m
The correct answer is: 24
The vibrations of a string of length 60 cm fixed at both ends are represented by the equation
where x and y are in cm and t in seconds. What is the maximum displacement of point x = 5cm ?
The given equation is :
This can be written as :
This shows that a = 2 cm, λ =30 cm and ω = 1440 cm/s
The maximum displacement is given by :
For x = 5 cm
The correct answer is: 3.464
A transverse harmonic wave of amplitude 0.02 m is generated at one end (x = 0) along horizontal string by a tuning fork of frequency 500 Hz. At a given instant of time, the displacement of the particle at x = 0.1 m is 0.005 m and that of the particle at x = 0.2 m is 0.005 m. Calculate the wavelength of the wave?
The general equation of this wave is given by
Here A = 0.02 m
Again, when x = 0.1m, y = 0.005 m
or
Again x = 0.2m, y = 0.005m
or λ = 0.2m
The correct answer is: 0.2
Equations of a stationary and a travelling waves are as follows :
The phase difference between two points respectively for the two waves. The ratio is :
sin kx_{1}, or sin kx_{2} is not zero.
Therefore, neither of x_{1} or x_{2} is a node
The correct answer is: 0.857
A simple harmonic wave travelling xaxis is given by y = 5 sin 2π ( 0.2t  0.5x) [x is in m and t in s]. Calculate the amplitude (in m ).
Here
But the standard progressive wave equation is :
Comparing equation (i) and (ii), we have
A = 5cm
The correct answer is: 5/100
= 0.05m
The equation for the vibration of a string fixed at both ends vibrating in its third harmonic is given by :
The length of the string is :
Wave number
or
The correct answer is: 15.7
A wave of frequency 400 Hz is travelling with a velocity 800 m/s. How far are two points situated whose displacement differs in phase by ?
The amplitude of wave disturbance propagating in positive xaxis is given by at t = 0 andat t= 2s, where x and y are in meters. The shape of the disturbance does not change during the propagation. The velocity (in m/s) of the wave is :
The given pulse is of the form
where v is the wave velocity
Given equation is
Comparing eq. (1) and (2), we get
The correct answer is: 0.5
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